a nitsche stabilized finite element method for frictional sliding on embedded interfaces part ii intersecting interfaces abstract we extend the weighted nitsche s method proposed in the first part of this study to include multiple intersecting embedded interfaces these intersections arise either inside a computational domain where two internal interfaces intersect or on the boundary of the computational domain where an internal interface intersects with the external boundary we propose a variational treatment of both the interfacial kinematics and the external dirichlet constraints within nitsche s framework we modify the numerical analysis to account for these intersections and provide an explicit expression for the weights and the method parameters that arise in the nitsche variational form in the presence of junctions finally we demonstrate the performance of the method for both perfectly tied interfaces and perfectly plastic sliding interfaces through several benchmark examples

consistent labeling problems and their algorithms expected complexities and theory based heuristics a new parameter is introduced to characterize a type of search problem of broad relevance in artificial intelligence operations research and symbolic logic this parameter which we call inter variable compatibility is particularly important in that complexity analyses incorporating it are able to capture the dependence of problem complexity on search order used by an algorithm thus compatibility based theories can provide a theoretical basis for the extraction of heuristics for choosing good search orderings a long sought goal for such problems since it can lead to significant savings during search we carry out expected complexity analyses for the traditional backtrack algorithm as well as for two more recent algorithms that have been found empirically to be significant improvements forward checking and word wise forward checking we extract compatibility based ordering heuristics from the theory for forward checking preliminary experimental results are presented showing the large savings that result from their use similar savings can be expected for other algorithms when heuristics taking account of inter variable compatibilities are used our compatibility based theories also provide a more precise way of predicting which algorithm is best for a given problem

a robust nitsche s formulation for interface problems abstract in this work we propose a novel weighting for the interfacial consistency terms arising in a nitsche variational form we demonstrate through numerical analysis and extensive numerical evidence that the choice of the weighting parameter has a great bearing on the stability of the method consequently we propose a weighting that results in an estimate for the stabilization parameter such that the method remains well behaved in varied settings ranging from the configuration of embedded interfaces resulting in arbitrarily small elements to such cases where a large contrast in material properties exists an important consequence of this weighting is that the bulk as well as the interfacial fields remain well behaved in the presence of a elements with arbitrarily small volume fractions b large material heterogeneities and c both large heterogeneities as well as arbitrarily small elements we then highlight the accuracy and efficiency of the proposed formulation through numerical examples focusing particular attention on interfacial quantities of interest

convergence of the finite difference scheme for a general class of the spatial segregation of reaction diffusion systems abstract in this work we prove convergence of the finite difference scheme for equations of stationary states of a general class of the spatial segregation of reaction diffusion systems with m 2 components more precisely we show that the numerical solution u h l given by the difference scheme converges to the l t h component u l when the mesh size h tends to zero provided u l c 2 for every l 1 2 m in particular our proof provides convergence of a difference scheme for the multi phase obstacle problem

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

appending boundary conditions by lagrange multipliers analysis of the lbb condition this paper is concerned with the analysis of discretization schemes for second order elliptic boundary value problems when essential boundary conditions are enforced with the aid of lagrange multipliers specifically we show how the validity of the ladyskaja babusska brezzi lbb condition for the corresponding saddle point problems depends on the various ingredients of the involved discretizations the main result states that the lbb condition is satisfied whenever the discretization step length on the boundary h gamma sim 2 ell is somewhat bigger than the one on the domain h omega sim 2 j this is quantified through constants stemming from the trace theorem norm equivalences for the multiplier spaces on the boundary and direct and inverse inequalities in order to better understand the interplay of these constants we then specialize the setting to wavelet discretizations in this case the stability criteria can be stated solely in terms of spectral properties of wavelet representations of the trace operator we conclude by illustrating our theoretical findings by some numerical experiments we stress that the results presented here apply to any spatial dimension and to a wide selection of lagrange multiplier spaces which in particular need not be traces of the trial spaces however we do always assume that a hierarchy of nested trial spaces is given

on some techniques for approximating boundary conditions in the finite element method we discuss the stabilization of finite element methods in which essential boundary conditions are approximated by babuska s method of lagrange multipliers and we show that there is a close connection with this technique and a classical method by nitsche

the fixed mesh ale approach for the numerical approximation of flows in moving domains in this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization and therefore the formulation to be presented falls within the category of fixed grid methods even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed grid method our approach can be applied together with any technique to impose approximately boundary conditions although we also describe the one we actually favor our main concern is to properly account for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian framework the distinctive feature being that at each time step results are projected onto a fixed background mesh that is where the problem is actually solved

nearly h1 optimal finite element methods abstract we examine the problem of finding the h 1 projection onto a finite element space of an unknown field satisfying a specified boundary value problem solving the projection problem typically requires knowing the exact solution we circumvent this issue and obtain a petrov galerkin formulation which achieves h 1 optimality requiring weighting functions to be defined locally on the element level permits only approximate h 1 optimality in multi dimensional configurations we investigate the relation between our formulation and other stabilized fem formulations we show in particular that our formulation leads to a derivation of the supg method in special cases the present formulation reduces to that of residual free bubbles finally we present guidelines for obtaining the petrov weight functions and include a numerical example for the helmholtz equation

an embedded dirichlet formulation for 3d continua this paper presents a new approach for imposing dirichlet conditions weakly on non fitting finite element meshes such conditions also called embedded dirichlet conditions are typically but not exclusively encountered when prescribing dirichlet conditions in the context of the extended finite element method xfem the methods key idea is the use of an additional stress field as the constraining lagrange multiplier function the resulting mixed hybrid formulation is applicable to 1d 2d and 3d problems the method does not require stabilization for the lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level furthermore only non zero diagonal terms are present in the tangent stiffness which allows the straight forward application of state of the art iterative solvers like algebraic multigrid amg techniques within this paper the method is applied to the linear momentum equation of an elastic continuum and to the transient incompressible navier stokes equations steady and unsteady benchmark computations show excellent agreement with reference values the general formulation presented in this paper can also be applied to other continuous field problems

determining if fc conflict directed back jumping visits a given node is np hard conflict directed back jumping is a modification of the backtracking algorithm that can outperform forward checking in non pathological examples we prove it is in general np hard to determine if back jumping or conflict directed back jumping or their forward checking hybrids visit a given node of a search space this shows that these algorithms are fundamentally more complex to analyze than backtracking and forward checking we conclude by describing how similar results can e proved for versions of the maintaining arc consistency algorithm 001 elsevier science b v all rights reserve

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

backjumping for quantified boolean logic satisfiability the implementation of effective reasoning tools for deciding the satisfiability of quantified boolean formulas qbfs is an important research issue in artificial intelligence many decision procedures have been proposed in the last few years most of them based on the davis logemann loveland procedure dll for propositional satisfiability sat in this paper we show how it is possible to extend the conflict directed backjumping schema for sat to the satisfiability of qbfs when applicable conflict directed backjumping allows search to skip over existentially quantified literals while backtracking we introduce solution directed backjumping which allows the same behavior for universally quantified literals we show how it is possible to incorporate both conflict directed and solution directed backjumping in a dll based decision procedure for satisfiability of qbfs we also implement and test the procedure the experimental analysis shows that because of backjumping significant speed ups can be obtained summing up we present the first algorithm that applies conflict and solution directed backjumping to qbf and demonstrate the performance of this algorithm via an empirical study

a symmetric method for weakly imposing dirichlet boundary conditions in embedded finite element meshes summary in this paper we propose a way to weakly prescribe dirichlet boundary conditions in embedded finite element meshes the key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation relatively small and can be fixed a priori moreover the formulation is symmetric for symmetric problems an additional element discontinuous stress field is used to enforce the boundary conditions in the poisson problem additional terms are required in order to guarantee stability in the convection diffusion equation and the stokes problem the proposed method is then easily extended to the transient navier stokes equations copyright 2012 john wiley sons ltd

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

an l 1 penalty method for general obstacle problems we construct an efficient numerical scheme for solving obstacle problems in divergence form the numerical method is based on a reformulation of the obstacle in terms of an l 1 like penalty on the variational problem the reformulation is an exact regularizer in the sense that for a large but finite penalty parameter we recover the exact solution our formulation is applied to classical elliptic obstacle problems as well as some related free boundary problems for example the two phase membrane problem and the hele shaw model one advantage of the proposed method is that the free boundary inherent in the obstacle problem arises naturally in our energy minimization without any need for problem specific or complicated discretization in addition our scheme also works for nonlinear variational inequalities arising from convex minimization problems

superconvergence analysis of approximate boundary flux calculations certain projection post processing techniques have been proposed for computing the boundary flux for two dimensional problems e g see carey et al 5 in a series of numerical experiments on elliptic problems they observed that these post processing formulas for approximate fluxes were almost o h 2 accurate for linear triangular elements in this paper we prove that the computed boundary flux iso h 2 ln 1 h accurate in the maximum norm for the partial method of 5 if the solutionu h 3 then the boundary flux error iso h 3 2 in thel 2 norm

a numerical approach for a general class of the spatial segregation of reaction diffusion systems arising in population dynamics abstract in the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction diffusion systems with m 2 population densities we introduce a discrete multi phase minimization problem related to the segregation problem which allows to prove the existence and uniqueness of the corresponding finite difference scheme based on that scheme we suggest an iterative algorithm and show its consistency and stability for the special case m 2 we show that the problem gives rise to the generalized version of the so called two phase obstacle problem in this particular case we introduce the notion of viscosity solutions and prove convergence of the difference scheme to the unique viscosity solution at the end of the paper we present computational tests for different internal dynamics and discuss numerical results

a bubble stabilized finite element method for dirichlet constraints on embedded interfaces we examine a bubble stabilized finite element method for enforcing dirichlet constraints on embedded interfaces by embedded we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh as such the robust imposition of dirichlet constraints using a lagrange multiplier field is not trivial to focus issues we consider a simple one sided problem that is representative of a wide class of evolving interface problems the bulk field is decomposed into coarse and fine scales giving rise to coarse scale and fine scale one sided sub problems the fine scale solution is approximated with bubble functions permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method importantly the method is simple to implement readily extends to multiple dimensions obviates the need to specify any free stabilization parameters and can lead to a symmetric positive definite system of equations the performance of the method is then examined through several numerical examples the accuracy of the lagrange multiplier is compared to results obtained using a local version of the domain integral method the variational multiscale approach proposed herein is shown to both stabilize the lagrange multiplier and improve the accuracy of the post processed fluxes copyright 2006 john wiley sons ltd

concurrent search for distributed csps a distributed concurrent search algorithm for distributed constraint satisfaction problems discsps is presented concurrent search algorithms are composed of multiple search processes sps that operate concurrently and scan non intersecting parts of the global search space each sp is represented by a unique data structure containing a current partial assignment cpa that is circulated among the different agents search processes are generated dynamically started by the initializing agent and by any number of agents during search in the proposed concdb algorithm all search processes perform dynamic backtracking as a consequence of backjumping a search space can be found unsolvable by a different search process this enhances the efficiency of the concdb algorithm concurrent dynamic backtracking is an asynchronous distributed algorithm and is shown to be faster than former algorithms for solving discsps experimental evaluation of concdb on randomly generated discsps demonstrates that the network load of concdb is similar to the network load of synchronous backtracking and is much lower than that of asynchronous backtracking the advantage of concurrent search is more pronounced in the presence of imperfect communication when messages are randomly delayed

an unfitted finite element method based on nitsche s method for elliptic interface problems in this paper we propose a method for the finite element solution of elliptic interface problem using an approach due to nitsche the method allows for discontinuities internal to the elements in the approximation across the interface we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh further we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples

an energy minimization finite element approach for the frank oseen model of nematic liquid crystals this paper outlines an energy minimization finite element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects the method targets minimization of the system free energy based on the frank oseen free energy model solutions to the intermediate discretized free elastic linearizations are shown to exist generally and are unique under certain assumptions this requires proving continuity coercivity and weak coercivity for the accompanying appropriate bilinear forms within a mixed finite element framework error analysis demonstrates that the method constitutes a convergent scheme numerical experiments are performed for problems with a range of physical parameters as well as simple and patterned boundary conditions the resulting algorithm accurately handles heterogeneous constant coefficients and effectively resolves configurations resulting from complicated boundary conditions relevant in ongoing research

hybrid backtracking bounded by tree decomposition of constraint networks we propose a framework for solving csps based both on backtracking techniques and on the notion of tree decomposition of the constraint networks this mixed approach permits us to define a new framework for the enumeration which we expect that it will benefit from the advantages of two approaches a practical efficiency of enumerative algorithms and a warranty of a limited time complexity by an approximation of the tree width of the constraint networks finally experimental results allow us to show the advantages of this approach

high order x fem and levelsets for complex microstructures uncoupling geometry and approximation in this contribution a strategy is proposed for uncoupling geometrical description and approximation with the x fem the strategy is based on an uniform coarse mesh that defines a high order approximation of the mechanical fields and an adapted mesh that defines the geometrical features by means of levelsets the connection between the geometry and the approximation is obtained by sharing the quadtree trees of the two meshes numerical examples involving level set based parts convergence studies mechanical computations and numerical homogenization show good promise for this approach

binary vs non binary constraints there are two well known transformations from non binary constraints to binary constraints applicable to constraint satisfaction problems csps with finite domains the dual transformation and the hidden variable transformation we perform a detailed formal comparison of these two transformations our comparison focuses on two backtracking algorithms that maintain a local consistency property at each node in their search tree the forward checking and maintaining arc consistency algorithms we first compare local consistency techniques such as arc consistency in terms of their inferential power when they are applied to the original non binary formulation and to each of its binary transformations for example we prove that enforcing arc consistency on the original formulation is equivalent to enforcing it on the hidden transformation we then extend these results to the two backtracking algorithms we are able to give either a theoretical bound on how much one formulation is better than another or examples that show such a bound does not exist for example we prove that the performance of the forward checking algorithm applied to the hidden transformation of a problem is within a polynomial bound of the performance of the same algorithm applied to the dual transformation of the problem our results can be used to help decide if applying one of these transformations to all or part of a constraint satisfaction model would be beneficial

approximate imposition of boundary conditions in immersed boundary methods we analyze several possibilities to prescribe boundary conditions in the context of immersed boundary methods as basic approximation technique we consider the finite element method with a mesh that does not match the boundary of the computational domain and therefore dirichlet boundary conditions need to be prescribed in an approximate way as starting variational approach we consider nitsche s methods and we then move to two options that yield non symmetric problems but that turned out to be robust and efficient the essential idea is to use the degrees of freedom of certain nodes of the finite element mesh to minimize the difference between the exact and the approximated boundary condition

a theoretical evaluation of selected backtracking algorithms abstract in recent years many new backtracking algorithms for solving constraint satisfaction problems have been proposed the algorithms are usually evaluated by empirical testing this method however has its limitations our paper adopts a different purely theoretical approach which is based on characterizations of the sets of search tree nodes visited by the backtracking algorithms a notion of inconsistency between instantiations and variables is introduced and is shown to be a useful tool for characterizing such well known concepts as backtrack backjump and domain annihilation the characterizations enable us to a prove the correctness of the algorithms and b partially order the algorithms according to two standard performance measures the number of nodes visited and the number of consistency checks performed among other results we prove the correctness of backjumping and conflict directed backjumping and show that forward checking never visits more nodes than backjumping our approach leads us also to propose a modification to two hybrid backtracking algorithms backmarking with backjumping bmj and backmarking with conflict directed backjumping bm cbj so that they always perform fewer consistency checks than the original algorithms

applications of the pseudo residual free bubbles to the stabilization of convection diffusion problems abstract residual free bubbles have been recently introduced in order to compute optimal values for the stabilization methods a la hughes franca however unless in very special situations one dimensional problems limit cases etc they require the actual solution of pde problems the bubble problems in each element thus they are very difficult to be used in practice in this paper we present for the special case of convection dominated elliptic problems a cheap way to compute approximately the solution of the bubble problem in each element this provides as a consequence a cheap way to compute good approximations for the optimal values of the stabilization parameters

the shifted boundary method for embedded domain computations part i poisson and stokes problems abstract we propose a new finite element method for embedded domain computations which falls in the category of surrogate approximate boundary algorithms the key feature of the proposed approach is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary and to appropriately modify the shifted boundary conditions enforced weakly in order to preserve optimal convergence rates of the numerical solution this process yields a method which in our view is simple efficient and also robust since it is not affected by the small cut cell problem although general in nature here we apply this new concept to the poisson and stokes problems we present in particular the full analysis of stability and convergence for the case of the poisson operator and numerical tests for both the poisson and stokes equations for geometries of progressively higher complexity

hierarchical enrichment for bridging scales and mesh free boundary conditions the finite element method when used with a basis made up of piecewise polynomials often requires the generation of a very fine computational mesh in order to capture localized solution phenomena such as boundary layers or near singularities enrichment of the basis with additional functions obtained through analytical or experimental means can allow for a coarser mesh and more accurate solution we introduce an enrichment scheme in which an interaction or bridging scale term is used to separate the basis formed by the enrichment functions from the original set of basis functions in effect making the enrichment hierarchical this separation of scales allows the simple application of essential boundary conditions it also allows a quantification of the effects of the enrichment leading to strategies for error estimation and control of the stiffness matrix condition number we also find that this formulation allows for the simple application of essential boundary conditions for mesh free shape functions which are notoriously problematic we find that for multiple dimensions care must be taken to derive a weak form which is truly consistent with the strong form on the essential boundary copyright 2001 john wiley sons ltd

on forward checking for non binary constraint satisfaction solving non binary constraint satisfaction problems a crucial challenge today can be tackled in two different ways translating the non binary problem into an equivalent binary one or extending binary search algorithms to solve directly the original problem the latter option raises some issues when we want to extend definitions written for the binary case this paper focuses on the well known forward checking algorithm and shows that it can be generalized to several non binary versions all fitting its binary definition the classical non binary version proposed by van hentenryck is only one of these generalizations

further considerations on residual free bubbles for advective diffusive equations abstract we further consider the galerkin method for advective diffusive equations in two dimensions the finite dimensional space employed is of piecewise polynomials enriched with residual free bubbles rfb we show that in general this method does not coincide with the supg method unless the piecewise polynomials are spanned by linear functions furthermore a simple stability analysis argument displays the effect of the rfb on the reduced space of piecewise polynomials which in some situations is not equivalent to streamline diffusion for bilinears

a numerical method for a second gradient theory of incompressible fluid flow this work concerns the development of a finite element method for discretizing a recent second gradient theory for the flow of incompressible fluids the new theory gives rise to a flow equation involving higher order gradients of the velocity field and introduces an accompanying length scale and boundary conditions finite element methods based on similar equations involving fourth order differential operators typically rely on c 1 continuous basis functions or a mixed approach both of which entail certain implementational difficulties here we examine the adaptation of a relatively inexpensive non conforming method based on c 0 continuous basis functions we first develop the variational form of the method and establish consistency the method weakly enforces continuity of the vorticity traction and hypertraction across interelement boundaries stabilization is achieved via nitsche s method further pressure stabilization scales with the higher order moduli so that the classical formulation is recovered as a particular limit the numerical method is verified for the problem of steady plane poiseuille flow we then provide several numerical examples illustrating the robustness of the method and contrasting the predictions to those provided by classical navier stokes theory

a high order immersed boundary discontinuous galerkin method for poisson s equation with discontinuous coefficients and singular sources author s brandstetter g govindjee s abstract 2014 john wiley a sons ltd we adopt a numerical method to solve poisson s equation on a fixed grid with embedded boundary conditions where we put a special focus on the accurate representation of the normal gradient on the boundary the lack of accuracy in the gradient evaluation on the boundary is a common issue with low order embedded boundary methods whereas a direct evaluation of the gradient is preferable one typically uses post processing techniques to improve the quality of the gradient here we adopt a new method based on the discontinuous galerkin dg finite element method inspired by the recent work of a j lew and g c buscaglia a discontinuous galerkin based immersed boundary method international journal for numerical methods in engineering 76 427 454 2008 the method has been enhanced in two aspects firstly we approximate the boundary shape locally by higher order geometric primitives secondly we employ higher order shape functions within intersected elements these are derived for the various geometric features of the boundary based on analytical solutions of the underlying partial differential equation the development includes three basic geometric features in two dimensions for the solution of poisson s equation a straight boundary a circular boundary and a boundary with a discontinuity we demonstrate the performance of the method via analytical benchmark examples with a smooth circular boundary as well as in the presence of a singularity due to a re entrant corner results are compared to a low order extended finite element method as well as the dg method of 1 we report improved accuracy of the gradient on the boundary by one order of magnitude as well as improved convergence rates in the presence of a singular source in principle the method can be extended to three dimensions more complicated boundary shapes and other partial differential equations

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

variational multiscale analysis the fine scale green s function projection optimization localization and stabilized methods we derive an explicit formula for the fine scale green s function arising in variational multiscale analysis the formula is expressed in terms of the classical green s function and a projector which defines the decomposition of the solution into coarse and fine scales the theory is presented in an abstract operator format and subsequently specialized for the advection diffusion equation it is shown that different projectors lead to fine scale green s functions with very different properties for example in the advection dominated case the projector induced by the h 1 0 seminorm produces a fine scale green s function which is highly attenuated and localized these are very desirable properties in a multiscale method and ones that are not shared by the l 2 projector by design the coarse scale solution attains optimality in the norm associated with the projector this property combined with a localized fine scale green s function indicates the possibility of effective methods with local character for dominantly hyperbolic problems the constructs lead to a new class of stabilized methods and the relationship between h 1 0 optimality and the streamline upwind petrov galerkin supg method is described

residual free bubbles for embedded dirichlet problems abstract we examine a stabilized method employing residual free bubbles for enforcing dirichlet constraints on embedded finite element interfaces in particular we focus attention on problems where the underlying mesh is not explicitly fitted to the geometry of the interface the residual free bubble problem is derived for a simple case and extensions are discussed we show that under certain conditions stabilization only requires knowledge of the residual free bubble on the interface we then examine methods to approximate the residual free bubble a series of benchmark tests are used to demonstrate the accuracy and robustness of the method comparisons are made to nitsche s method employing an eigenvalue estimate for the global stability parameter particular emphasis is placed on the accuracy of flux evaluations on the interface finally we employ the method to simulate an evolving interface problem motivated by resin transfer molding

approximate boundary flux calculations abstract a technique for determining derivatives fluxes or stresses from finite element solutions is developed the approach is a generalization to higher dimensions of a procedure known to give highly accurate results in one dimension numerical experiments demonstrate that certain difficulties are associated with corners in the higher dimensional extensions and two variants of the method are examined we consider both triangular and quadrilateral elements and observe some interesting differences in the numerical rates of convergence finally this post processing scheme is tested for nonlinear problems

sparse low energy decomposition for viscous conservation laws for viscous conservation laws solutions contain smooth but high contrast features which require the use of fine grids to properly resolve on coarse grids these high contrast jumps resemble shocks rather than their true viscous profiles which could lead to issues in the numerical approximation of their underlying dynamics in many cases the equations of motion emit traveling wave solutions which can be used to represent the viscous profiles analytically the traveling wave solutions can be thought of as a lower dimensional representation of the motion since they contain information from the evolution equation but are constant along certain time space curves using a parameterized basis involving the traveling waves along with the sparse low energy decompositions found in imaging sciences we propose an approximation to viscous conservation laws which separates the coarse smooth component from the sharp fine one our method provides an appropriate approximation to the solution on a coarse grid thereby accurately under resolving the viscous profile this is similar to the philosophy of shock capturing methods in the sense that we want to capture the viscous front without needing to resolve the profile theoretical results on the consistency of our method are shown in general we provide several computational examples for convex and non convex fluxes

immersed finite element method abstract in this paper the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models in ifem a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain hence the mesh generation is greatly simplified moreover both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method rkpm delta function in comparison with the immersed boundary ib method the higher ordered rkpm delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions the use of such kernel functions may eventually open doors to multi scale and multi resolution modelings of complex fluid structure interaction problems rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method the results compare well with the experimental data to the authors knowledge these are the first solutions that deal with particulate flows with very flexible solids

imposing essential boundary conditions in mesh free methods imposing essential boundary conditions is a key issue in mesh free methods the mesh free interpolation does not verify the kronecker delta property and therefore the imposition of prescribed values is not as straightforward as for the finite element method the aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in galerkin based mesh free methods special attention is paid to the mesh free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the galerkin weak form particular examples are used to analyze and compare their performance in different situations

a second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions we present a numerical method for the variable coefficient poisson equation in three dimensional irregular domains and with interfacial discontinuities the discretization embeds the domain and interface into a uniform cartesian grid augmented with virtual degrees of freedom to provide accurate treatment of jump and boundary conditions the matrix associated with the discretization is symmetric positive definite and equal to the standard 7 point finite difference poisson stencil away from embedded interfaces and boundaries numerical evidence suggests second order accuracy in the l norm our approach improves the treatment of dirichlet and jump constraints in the recent work of bedrossian et al 1 and introduces innovations necessary in three dimensions specifically we construct new constraint based lagrange multiplier spaces that significantly improve the conditioning of the associated linear system of equations we provide a method for cell local polyhedral approximation to the zero isocontour surface of a level set needed for three dimensional embedding and we show that the new lagrange multiplier spaces naturally lead to a class of easy to implement multigrid methods that achieve near optimal efficiency as shown by numerical examples for the specific case of a continuous poisson coefficient in interface problems we provide an expansive treatment of the construction of a particular solution that satisfies the value jump and flux jump constraints as in 1 this is used in a discontinuity removal technique that yields the standard 7 point stencil across the interface and only requires a modification to the right hand side of the linear system

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

towards multiscale functions enriching finite element spaces with local but not bubble like functions in this paper we propose a novel way via finite elements to treat problems that can be singular perturbed a reaction diffusion equation in our case we enrich the usual piecewise linear or bilinear finite element trial spaces with local solutions of the original problem as in the residual free bubble rfb setting but do not require these functions to vanish on each element edge a departure from the rfb paradigm such multiscale functions have an analytic expression for triangles and rectangles bubbles are the choice for the test functions allowing static condensation thus our method is of petrov galerkin type we perform several numerical validations which confirm the good performance of the method 2004 elsevier b v all rights reserved

on methods for stabilizing constraints over enriched interfaces in elasticity summary enriched finite element approaches such as the extended finite element method provide a framework for constructing approximations to solutions of non smooth problems internal features such as boundaries are represented in such methods by using discontinuous enrichment of the standard finite element basis within such frameworks however imposition of interface constraints and or constitutive relations can cause unexpected difficulties depending upon how relevant fields are interpolated on un gridded interfaces this work address the stabilized treatment of constraints in an enriched finite element context both the lagrange multiplier and penalty enforcement of tied constraints for an arbitrary boundary represented in an enriched finite element context can lead to instabilities and artificial oscillations in the traction fields we demonstrate two alternative variational methods that can be used to enforce the constraints in a stable manner in a bubble stabilized approach fine scale degrees of freedom are added over elements supporting the interface the variational form can be shown to have a similar form to a second approach we consider nitsche s method with the exception that the stabilization terms follow directly from the bubble functions in this work we examine alternative variational methods for enforcing a tied constraint on an enriched interface in the context of two dimensional elasticity we examine several benchmark problems in elasticity and show that only nitsche s method and the bubble stabilization approach produce stable traction fields over internal boundaries we also demonstrate a novel difference between the penalty method and nitsche s method in that the latter passes the patch test exactly regardless of the stabilization parameter s magnitude results for more complicated geometries and triple interface junctions are also presented copyright 2008 john wiley sons ltd

the shifted boundary method for embedded domain computations part ii linear advection diffusion and incompressible navier stokes equations abstract we propose a new embedded finite element method for the linear advection diffusion equation and the laminar and turbulent incompressible navier stokes equations the proposed method belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates we include the full analysis of stability and convergence of the method in the linear advection diffusion equation and a battery of tests for the case of laminar and turbulent incompressible navier stokes equations we also discuss the conservation properties of the proposed method in all cases

a contact algorithm for frictional crack propagation with the extended finite element method we present an incremental quasi static contact algorithm for path dependent frictional crack propagation in the framework of the extended finite element fe method the discrete formulation allows for the modeling of frictional contact independent of the fe mesh standard coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity the contact constraint is borrowed from non linear contact mechanics and embedded within a localized element by penalty method newton raphson iteration with consistent linearization is used to advance the solution we show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called latin for frictional crack propagation numerical examples include simulation of crack initiation and propagation in 2d plane strain with and without bulk plasticity in the presence of bulk plasticity the problem is also solved using an augmented lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution copyright 2008 john wiley sons ltd

enhancement schemes for constraint processing backjumping learning and cutset decomposition abstract researchers in the areas of constraint satisfaction problems logic programming and truth maintenance systems have suggested various schemes for enhancing the performance of the backtracking algorithm this paper defines and compares the performance of three such schemes backjumping learning and cycle cutset the backjumping and the cycle cutset methods work best when the constraint graph is sparse while the learning scheme mostly benefits problem instances with dense constraint graphs an integrated strategy is described which utilizes the distinct advantages of each scheme experiments show that in hard problems the average improvement realized by the integrated scheme is 20 25 higher than any of the individual schemes

finite element analysis on implicitly defined domains an accurate representation based on arbitrary parametric surfaces in this paper we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis the novel contributions of this paper are threefold 1 describe and validate a method to represent arbitrary parametric surfaces implicitly 2 represent arbitrary solids implicitly including sharp features using level sets and boolean operations 3 impose arbitrary dirichlet and neumann boundary conditions on the resulting implicitly defined boundaries the methods proposed do not require local refinement of the finite element mesh in regions of high curvature ensure the independence of the domain s volume on the mesh do not rely on boundary regularization and are well suited to methods based on fixed grids such as the extended finite element method xfem numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries this approach is one step in the desired direction of tying numerical simulations to computer aided design cad similarly to the isogeometric analysis paradigm

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

residual free bubbles for the helmholtz equation the galerkin method enriched with residual free bubbles is considered for approximating the solution of the helmholtz equation two dimensional tests demonstrate the improvement over the standard galerkin method and the galerkin least squares method using piecewise bilinear interpolations

an extended finite element method with algebraic constraints xfem ac for problems with weak discontinuities abstract we present a new extended finite element method with algebraic constraints xfem ac for recovering weakly discontinuous solutions across internal element interfaces if necessary cut elements are further partitioned by a local secondary cut into body fitting subelements each resulting subelement contributes an enrichment of the parent element the enriched solutions are then tied using algebraic constraints which enforce c 0 continuity across both cuts these constraints impose equivalence of the enriched and body fitted finite element solutions and are the key differentiating feature of the xfem ac in so doing a stable mixed formulation is obtained without having to explicitly construct a compatible lagrange multiplier space and prove a formal inf sup condition likewise convergence of the xfem ac solution follows from its equivalence to the interface fitted finite element solution this relationship is further exploited to improve the numerical solution of the resulting xfem ac linear system examples are shown demonstrating the new approach for both steady state and transient diffusion problems

energy minimization for liquid crystal equilibrium with electric and flexoelectric effects this paper outlines an energy minimization finite element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields the method targets minimization of free energy based on the electrically and flexoelectrically augmented frank oseen free energy models the hessian resulting from the linearization of the first order optimality conditions is shown to be invertible for both models when discretized by a mixed finite element method under certain assumptions this implies that the intermediate discrete linearizations are well posed a coupled multigrid solver with vanka type relaxation is proposed and numerically vetted for approximation of the solution to the linear systems arising in the linearizations two electric model numerical experiments are performed with the proposed multigrid solver the first compares the algorithm s solution of a classical freedericksz transition problem to the known analytical solution and demons

a numerical strategy for investigating the kinetic response of stimulus responsive hydrogels we present a strategy for obtaining numerical solutions to a system of non linear coupled evolution equations describing volume transitions in stimulus responsive hydrogels srhs the theory underlying our sharp interface model of phase transitions in srhs is provided along with the assumptions leading to the specialized formulation that is the starting point for the numerical method the discrete formulation is then developed with a hybrid extended finite element level set method xfe lsm domain integral methodologies are used consistently to extract interfacial quantities such as the mechanical driving traction the jump in the normal component of the solute flux and requisite geometric information several benchmark studies are provided to demonstrate the accuracy and robustness of the numerical strategy we then investigate various features of srh kinetics including the regimes of unstable and stable phase transitions surface pattern formation and bulk phase separation

backjump based backtracking for constraint satisfaction problems the performance of backtracking algorithms for solving finite domain constraint satisfaction problems can be improved substantially by look back and look ahead methods look back techniques extract information by analyzing failing search paths that are terminated by dead ends look ahead techniques use constraint propagation algorithms to avoid such dead ends altogether this paper describes a number of look back variants including backjumping and constraint recording which recognize and avoid some unnecessary explorations of the search space the last portion of the paper gives an overview of look ahead methods such as forward checking and dynamic variable ordering and discusses their combination with backjumping

a new formulation for imposing dirichlet boundary conditions on non matching meshes generating matching meshes for problems with complex boundaries is often an intricate process and the use of non matching meshes appears as an appealing solution yet enforcing boundary conditions on non matching meshes is not a straightforward process especially when prescribing those of dirichlet type by combining a type of generalized finite element method gfem with the lagrange multiplier method a new technique for the treatment of essential boundary conditions on non matching meshes is introduced in this manuscript the new formulation yields a symmetric stiffness matrix and is straightforward to implement as a result the methodology makes possible the analysis of problems with the use of simple structured meshes irrespective of the problem domain boundary through the solution of linear elastic problems we show that the optimal rate of convergence is preserved for piecewise linear finite elements yet the formulation is general and thus it can be extended to other elliptic boundary value problems

the shifted boundary method for hyperbolic systems embedded domain computations of linear waves and shallow water flows abstract we propose a new computational approach for embedded boundary simulations of hyperbolic systems and in particular the linear wave equations and the nonlinear shallow water equations the proposed approach belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates this framework is applied here in the setting of a stabilized finite element method even though other spatial discretization techniques could have been employed accuracy stability and robustness of the proposed method are tested by means of an extensive set of computational experiments for the acoustic wave propagation equations and shallow water equations comparisons with standard weak boundary conditions imposed on body fitted grids which conform to the geometry of the computational domain boundaries are also presented

primal interface formulation for coupling multiple pdes a consistent derivation via the variational multiscale method abstract this paper presents a primal interface formulation that is derived in a systematic manner from a lagrange multiplier method to provide a consistent framework to couple different partial differential equations pde as well as to tie together nonconforming meshes the derivation relies crucially on concepts from the variational multiscale vms approach wherein an additive multiscale decomposition is applied to the primary solution field modeling the fine scales locally at the interface using bubble functions consistent residual based terms on the boundary are obtained that are subsequently embedded into the coarse scale problem the resulting stabilized lagrange multiplier formulation is converted into a robust discontinuous galerkin dg method by employing a discontinuous interpolation of the multipliers along the segments of the interface as a byproduct analytical expressions are derived for the stabilizing terms and weighted numerical flux that reflect the jump in material properties governing equation or element geometry across the interface also a procedure is proposed for automatically generating the fine scale bubble functions that is inspired by a performance study of residual free bubbles for the interface problem a series of numerical tests confirms the robustness of the method for solving interface problems with heterogeneous elements materials and or governing equations and also highlights the benefit and importance of deriving the flux and stabilization terms

a second order virtual node method for elliptic problems with interfaces and irregular domains we present a second order accurate geometrically flexible and easy to implement method for solving the variable coefficient poisson equation with interfacial discontinuities or on irregular domains handling both cases with the same approach we discretize the equations using an embedded approach on a uniform cartesian grid employing virtual nodes at interfaces and boundaries a variational method is used to define numerical stencils near these special virtual nodes and a lagrange multiplier approach is used to enforce jump conditions and dirichlet boundary conditions our combination of these two aspects yields a symmetric positive definite discretization in the general case we obtain the standard 5 point stencil away from the interface for the specific case of interface problems with continuous coefficients we present a discontinuity removal technique that admits use of the standard 5 point finite difference stencil everywhere in the domain numerical experiments indicate second order accuracy in l

on the stability of residual free bubbles for convection diffusion problemsand their approximation by a two level finite element method we consider the galerkin finite element method for partial diffferential equations in two dimensions where the finite dimensional space used consists of piecewise isoparametric polynomials enriched with bubble functions writing l for the differential operator we show that for elliptic convection diffusion problems the component of the bubble enrichment that stabilizes the method is essentially equivalent to a petrov galerkin method with an l spline exponentially fitted trial space and piecewise polynomial test space the remaining component of the bubble influences the accuracy of the method a stability inequality recently obtained by brezzi franca and russo for a limiting case of bubbles applied to convection diffusion problems is shown to be slightly weaker than the standard stability inequality that is obtained for the sdfem supg method thereby demonstrating that the bubble approach is in general slightly less stable than the streamline diffusion method when the trial functions are piecewise linear we show that residual free bubbles are as stable as sdfem supg and we extend this stability inequality to include positive mesh peclet numbers in the convection dominated regime approximate computations of the residual free bubbles are performed using a two level finite element method

finite element analysis of inelastic laminated plates using a global local formulation with delamination abstract this work represents the initial step toward the development of an efficient computational framework that can be used to study the response and or failure of laminated composite plates under a variety of loading conditions including complex severe static and dynamic loads the proposed finite element formulation is based on the global local laminated plate theory of williams t o williams a generalized multilength scale non linear composite plate theory with delamination int j solids struct 36 20 1999 3015 3050 which is founded on a generalized superposition of displacement fields associated with different length scales the global field which spans the thickness of the plate and a set of local fields consistent with the layering thickness this global local strategy allows the local layerwise fields to be activated only in regions of critical interest within the computational domain to obtain accurate results in those regions without compromising overall computational efficiency in the present work attention is restricted to the geometrically linear case however the formulation allows treatment of problems involving non linear constitutive behavior and facilitates the incorporation of delamination kinematics several numerical examples are presented to examine the performance characteristics of the proposed global local plate element

a fem approximation of a two phase obstacle problem and its a posteriori error estimate this paper is concerned with the two phase obstacle problem a type of a variational free boundary problem we recall the basic estimates of repin and valdman 2015 and verify them numerically on two examples in two space dimensions a solution algorithm is proposed for the construction of the finite element approximation to the two phase obstacle problem the algorithm is not based on the primal convex and nondifferentiable energy minimization problem but on a dual maximization problem formulated for lagrange multipliers the dual problem is equivalent to a quadratic programming problem with box constraints the quality of approximations is measured by a functional a posteriori error estimate which provides a guaranteed upper bound of the difference of approximated and exact energies of the primal minimization problem the majorant functional in the upper bound contains auxiliary variables and it is optimized with respect to them to provide a sharp upper bound a space density of the nonlinear related part of the majorant functional serves as an indicator of the free boundary

stabilized low order finite elements for frictional contact with the extended finite element method abstract contact problem suffers from a numerical instability similar to that encountered in incompressible elasticity in which the normal contact pressure exhibits spurious oscillation this oscillation does not go away with mesh refinement and in some cases it even gets worse as the mesh is refined using a lagrange multipliers formulation we trace this problem to non satisfaction of the lbb condition associated with equal order interpolation of slip and normal component of traction in this paper we employ a stabilized finite element formulation based on the polynomial pressure projection ppp technique which was used successfully for stokes equation and for coupled solid deformation fluid diffusion using low order mixed finite elements for the frictional contact problem the polynomial pressure projection approach is applied to the normal contact pressure in the framework of the extended finite element method we use low order linear triangular elements tetrahedral elements for 3d for both slip and normal pressure degrees of freedom and show the efficacy of the stabilized formulation on a variety of plane strain plane stress and three dimensional problems

a multiscale finite element method for the incompressible navier stokes equations this paper presents a new multiscale finite element method for the incompressible navier stokes equations the proposed method arises from a decomposition of the velocity field into coarse resolved scales and fine unresolved scales modeling of the unresolved scales corrects the lack of stability of the standard galerkin formulation and yields a method that possesses superior properties like that of the streamline upwind petrov galerkin supg method and the galerkin least squares gls method the multiscale method allows arbitrary combinations of interpolation functions for the velocity and the pressure fields specifically the equal order interpolations that are easy to implement but violate the celebrated babuska brezzi condition a significant feature of the present method is that the structure of the stabilization tensor s appears naturally via the solution of the fine scale problem a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed convergence studies for the method on uniform skewed as well as composite meshes are presented numerical simulations of the nonlinear steady and transient flow problems are shown that exhibit the good stability and accuracy properties of the method 2005 elsevier b v all rights reserved

a multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within xfem in this paper we highlight that when the extended finite element method xfem is employed to model a microstructure in which inclusions are involved and the distance between two inclusions is small enough to be comparable with the mesh size three numerical artefacts are induced significantly affecting the convergence and accuracy of the numerical solution to the problem with such a microstructure these artefacts are a an artificial percolation of nearby inclusions b an artificial distortion of phase domains c an enrichment deficiency we propose to improve the xfem levelset method so as to avoid these artefacts the new technique leading to this improvement uses one level set function for each inclusion and adds additional enrichment in an element whose support is cut by several interfaces a local description of the multiple level sets is provided to avoid the storage of all level set functions a simple integration rule is employed for numerical quadrature in elements cut by several interfaces we show that the artefacts mentioned hereinbefore are circumvented in this framework the performances of the method are demonstrated through benchmarks and examples applied to the homogenization of concrete materials in 2d and 3d cases

on point duration networks for temporal reasoning we present here a point duration network formalism which extends the point algebra model to include additional variables that represent durations between points of time thereafter the new qualitative model is enlarged for allowing unary metric constraints on points and durations subsuming in this way several point based approaches to temporal reasoning we deal with some reasoning tasks within the new models and we show that the main problem deciding consistency is np complete however tractable special cases are identified and we show efficient algorithms for checking consistency finding a solution and obtaining the minimal network

modelling complex high speed multimaterial evolutions using a single mesh multivelocity strategy in the present paper we propose another space discretization of the kinematic constraint for a single grid multi velocity formulation leading to a better approximation of the interface physics the paper is organized as follows in the next section we will briefly review the problem to solve and the single mesh multi velocity discretization strategy in section 3 we will then introduce our new cell based discretization of the normal velocity continuity constraint on the interface develop the proper velocity enrichment and analyse its stability a generic time discretization is next introduced in section 4 and adapted to the specific space discretization proposed herein the proposed methodology is finally validated on a few numerical examples

backtracking algorithms for disjunctions of temporal constraints abstract we extend the framework of simple temporal problems studied originally by dechter meiri and pearl to consider constraints of the form x 1 y 1 r 1 x n y n r n where x 1 x n y 1 y n are variables ranging over the real numbers r 1 r n are real constants and n 1 this is a wide class of temporal constraints that can be used to model a variety of problems in temporal reasoning scheduling planning and temporal constraint databases we have implemented several progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints backtracking backjumping three variations of forward checking and forward checking with backjumping we have partially ordered the above algorithms according to the number of visited search nodes and the number of performed consistency checks although our problem is non binary our results agree with the results of kondrak and van beek who consider only binary constraints we have also studied the performance of the above algorithms experimentally using randomly generated sets of data and job shop scheduling problems the experiments with random instances allowed us to locate the hard region for this class of problems the results show that hard problems occur at a critical value of the ratio of disjunctions to variables

a stable lagrange multiplier space for stiff interface conditions within the extended finite element method this paper introduces a new algorithm to define a stable lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method in contrast to earlier approaches we do not work with an interior penalty formulation as e g for nitsche techniques but impose the constraints weakly in terms of lagrange multipliers roughly speaking a stable and optimal discrete lagrange multiplier space has to satisfy two criteria a best approximation property and a uniform inf sup condition owing to the fact that the interface does not match the edges of the mesh the choice of a good discrete lagrange multiplier space is not trivial here we propose a new algorithm for the local construction of the lagrange multiplier space and show that a uniform inf sup condition is satisfied a counterexample is also presented i e the inf sup constant depends on the mesh size and degenerates as it tends to zero numerical results in two dimensional confirm the theoretical ones copyright

a localized mixed hybrid method for imposing interfacial constraints in the extended finite element method xfem the paper proposes an approach for the imposition of constraints along moving or fixed immersed interfaces in the context of the extended finite element method an enriched approximation space enables consistent representation of strong and weak discontinuities in the solution fields along arbitrarily shaped material interfaces using an unfitted background mesh the use of lagrange multipliers or penalty methods is circumvented by a localized mixed hybrid formulation of the model equations in a defined region in the vicinity of the interface the original problem is re stated in its auxiliary formulation the availability of the auxiliary variable enables the consideration of a variety of interface constraints in the weak form the contribution discusses the weak imposition of dirichlet and neumann type interface conditions as well as continuity requirements not fulfilled a priori by the enriched approximation the properties of the proposed approach applied to two dimensional linear scalar and vector valued elliptic problems are investigated by studying the convergence behavior

parameter free weak imposition of dirichlet boundary conditions and coupling of trimmed and non conforming patches we present a parameter free domain sewing approach for low order as well as high order finite elements its final form contains only primal unknowns that is the approach does not introduce additional unknowns at the interface additionally it does not involve problem dependent parameters which require an estimation the presented approach is symmetry preserving that is the resulting discrete form of an elliptic equation will remain symmetric and positive definite it preserves the order of the underlying discretization and we demonstrate high order accuracy for problems of non matching discretizations concerning the mesh size h as well as the polynomial degree of the order of discretization p we also demonstrate how the method may be used to model material interfaces which may be curved and for which the interface does not coincide with the underlying mesh this novel approach is presented in the context of the p version and b spline version of the finite cell method an embedded domain method of high order and compared with more classical methods such as the penalty method or nitsche s method

the fixed mesh ale approach applied to solid mechanics and fluid structure interaction problems in this paper we propose a method to solve solid mechanics and fluid structure interaction problems using always a fixed background mesh for the spatial discretization the main feature of the method is that it properly accounts for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian ale framework the distinctive characteristic being that at each time step results are projected onto a fixed background mesh for solid mechanics problems subject to large strains the fixed mesh fm ale method avoids the element stretching found in fully lagrangian approaches for fsi problems fm ale allows for the use of a single background mesh to solve both the fluid and the structure copyright 2009 john wiley sons ltd

a discontinuous galerkin based immersed boundary method a numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced the proposed method is conceptually simple and free of user defined parameters starting with a conforming finite element mesh the key ingredient is to switch those elements intersected by the dirichlet boundary to a discontinuous galerkin approximation and impose the dirichlet boundary conditions strongly by virtue of relaxing the continuity constraint at those elements boundary locking is avoided and optimal order convergence is achieved this is shown through numerical experiments in reaction diffusion problems copyright 2008 john wiley sons ltd