structural instability analyses based on generalised path following this paper describes how quasi static conservative instability problems can be completely described using generalised path following procedures for augmented equilibrium formulations in particul

c1 continuous stress recovery in finite element analysis abstract a penalized discrete least squares pdls variational principle is employed to recover c 1 continuous smooth stress fields from finite element stresses the error functional involves discrete least squares with a penalty constraint to enforce c 1 continuity of the recovered stresses the recovery procedure uses a smoothing element analysis sea with element based interpolation functions to minimize the error functional sea pdls recovers a superconvergent stress field of higher accuracy and continuity than the underlying consistent finite element stress field general and specialized formulations of the functional are given and an appropriate discretization strategy for the sea is discussed numerical results for both one and two dimensional stress fields are presented and compared with the corresponding solutions for the superconvergent patch recovery spr method of zienkiewicz and zhu the results demonstrate that in addition to achieving a higher degree of continuity sea pdls produces generally more accurate stresses than spr although an additional global analysis is required results indicate that two coarse mesh analyses finite element and smoothing produce solutions comparable to a single finite element analysis with a much greater degree of refinement and more computational effort the procedure is unique in that the recovered stress field is essentially c 1 continuous the results are shown to be insensitive to the value of the penalty parameter above a threshold and hence uncertainty in the choice of an appropriate penalty value is eliminated

hierarchical bases give conjugate gradient type methods a multigrid speed of convergence the interesting properties of the discretization matrices arising in the finite element solution of plane elliptic boundary value problems when using hierarchical bases are described the condition numbers of these discretization matrices grow only quadratically in the number of refinement levels contrary to the exponential growth found with nodal bases furthermore it is easily possible to compute the product of such a discretization matrix with a given coefficient vector we show how these results can be used to solve the discretized problem in o n log n computer operations where n is the number of unknowns special emphasis is layed on the refinement structures used in r e bank s pltmg package which have not been treated in the author s previous papers

stopping distributions for right processes letx be a transient right process for which semipolar sets are polar we characterize the measures which can arise as the distribution ofx t witht a non randomized stopping time

models algorithms and error estimation for computational viscoelasticity this article reviews numerical algorithms for problems in solid polymer viscoelasticity in both small and large deformation for the linear small strain case we review both the quasistatic and the dynamic problem and give recent results on a posteriori error estimation for the large strain case we focus on the formulation and computational modelling of constrained membrane inflation the application of which is to the thermoforming process

computational methods for multiphase flow and reactive transport problems arising in subsurface contaminant remediation a mathematical formulation and some numerical approximation techniques are described for a system of coupled partial differential and algebraic equations describing multiphase flow transport and interactions of chemical species in the subsurface a parallel simulator parsim has been developed based on these approximation techniques and is being used to study contaminant remediation strategies numerical results for a highly complex geochemistry problem involving strontium disposal in a pit at oak ridge national laboratory are presented

the generalized finite element method for helmholtz equation theory computation and open problems in this paper we address the generalized finite element method for the helmholtz equation we obtain our method by employing the finite element method on cartesian meshes which may overlap the boundaries of the problem domain and by enriching the approximation by plane waves pasted into the finite element basis at each mesh vertex by the partition of unity method here we address the q convergence of the method where q is the number of plane waves added at each vertex for the class of smooth analytic solutions for which we get better than exponential convergence for sufficiently small h depending on p an important observation is that we can monitor the accuracy in any computed solution quantity of interest at negligible cost by using q extrapolation our results assume exact integration of all the employed integrals further studies are needed to analyze the effects of the numerical integrations and also the effect of the roundoff errors

a new bem fem coupling strategy for two dimensional fluid solid interaction problems we present a numerical method to solve a fluid solid interaction problem posed in the plane in this scheme we use a finite element method to approximate the solid vibrations and the near wave field the far field effects are taken into account by means of boundary integral equations posed on an artificial interface that contains the obstacle the boundary unknown involved in our formulation is approximated by a spectral method we obtain a fully discrete galerkin procedure whose main advantage is the simplicity of the quadratures used to approximate the weakly singular boundary integrals we provide numerical results that illustrate the accuracy of our method and the stability of the algorithm used to solve the linear systems of equations that arise from this discretization technique

a self optimizing single step algorithm for the numerical integration of parabolic equations abstract an unconditionally stable single step time marching algorithm for parabolic equations is presented in this algorithm time stepping parameters are chosen according to an error condition such that large time step accuracy is achieved and the solution is also free from oscillations it is different from conventional algorithms such as the crank nicolson scheme in that it uses a matrix of time stepping parameters rather than a single scalar value these parameters can be approximated inexpensively this algorithm is easily programmed and comparisons are made with other methods for different cases of a heat conduction problem it is found that the algorithm gives a more accurate solution for all degrees of freedom for the cases considered it is therefore advantageous over the conventional variably weighted euler method which has a constraint that the same value must be used for all degrees of freedom and that values have to be changed by trial and error for different time step sizes and mesh refinements in order to achieve best results

an improved variational method for finite element stress recovery and a posteriori error estimation abstract a new variational formulation is presented which serves as a foundation for an improved finite element stress recovery and a posteriori error estimation in the case of stress predictions interelement discontinuous stress fields from finite element solutions are transformed into a c 1 continuous stress field with c 0 continuous stress gradients these enhanced results are ideally suited for error estimation since the stress gradients can be used to assess equilibrium satisfaction the approach is employed as a post processing step in finite element analysis the variational statement used herein combines discrete least squares penalty constraint and curvature control functionals thus enabling automated recovery of smooth stresses and stress gradients the paper describes the mathematical foundation of the method and presents numerical examples including stress recovery in two dimensional structures and built up aircraft components and error estimation for adaptive mesh refinement procedures

wavelet based ilu preconditioners for the numerical solution by pufem of high frequency elastic wave scattering daubechies family of wavelets combined to the incomplete lower upper ilu factorization are considered as preconditioners for a block sparse linear system arising from the approximation of the time harmonic elastic wave equations by the partition of unity finite element method pufem after applying the discrete wavelet transform dwt to each dense block in the final matrix and the known right hand side due to the local enrichment by pressure p and shear s plane waves the resulting linear system is solved by the restarted generalized minimum residual method gmres with ilu preconditioners allowing fill in elements in the l and u matrix factors a reordering algorithm of the vertices based on gibbs method is also introduced it leads to a significant reduction of the bandwidth of the wave based finite element fe matrix and enables the ilu preconditioners to be more effective to study the performance of the proposed preconditioners a problem of a horizontal s plane wave scattered by a rigid circular body in an infinite elastic medium is considered the numerical tests show the good performance of the dwt based ilu preconditioners in improving the rate of convergence of gmres for high numbers of approximating p and s plane waves on coarse mesh grids containing multi wavelength sized elements moreover the haar dwt enhances the scalability with respect to the problem size when the number of the nodal points increases of the ilu preconditioner which uses the threshold strategy in the control of the fill in elements despite the high level of the conditioning a good accuracy may be achieved for a discretization level of around 1 9 degrees of freedom per s wavelength which is far below the rule of thumb of 10 nodal points per wavelength adopted for the conventional fe

a comparison of nrbcs for pufem in 2d helmholtz problems at high wave numbers in this work exact and approximate non reflecting boundary conditions nrbcs are implemented with the partition of unity finite element method pufem to solve short wave scattering problems governed by the helmholtz equation in two dimensions by short wave problems we mean situations in which the wavelength is a small fraction of the characteristic dimension of the scatterer various nrbcs are implemented and a comparison of their performance is carried out based on the accuracy of the results ease of implementation and computational cost the aim is to accurately model such problems in a reduced computational domain around the scatterer with fewer elements and without refining the mesh at each wave number

supernatural quad4 a template formulation abstract a universal template for a 4 node quadrilateral in plane stress is constructed using a combination of old and new techniques the use of natural quantities strongly advocated by j h argyris since his continua and discontinua 1965 exposition is further expanded the qualifier supernatural means that all governing equations kinematic constitutive and equilibrium are expressed in both cartesian and natural forms these two sets are used to build different components of the template with timely help from a computer algebra system a template that include all possible quadrilateral elements that pass the individual element test of bergan and hanssen emerges it yields an infinite number of hitherto undiscovered instances that may be customized to fit special needs a striking example is the construction of a two trapezoid macroelement that is bending exact about one direction for any amount of distortion this concludes a five decade search that begins with the formulation of the wing cover rectangular panel in argyris 1954 seminal serial on energy methods and structural analysis

derivative superconvergence of rectangular finite elements for the reissner mindlin plate abstract the finite element method with rectangular meshes for the reissner mindlin plate is analyzed for a plate with thickness bounded below by a positive constant moderately thick plate derivative superconvergence of the finite element solution at the gaussian points is justified and optimal error estimates for both rotation and displacement are established

riesz decompositions in markov process theory riesz decompositions of excessive measures and excessive functions are obtained by probabilistic methods without regularity assumptions the decomposition of excessive measures is given for borel right processes the results for excessive functions are formulated within the framework of weak duality these results extend and generalize the pioneering work of hunt in this area

a stable bilinear element for the reissner mindlin plate model abstract in this paper we introduce a new quadrilateral element using isoparametric bilinear basis functions for both components of the rotation vector and the deflection the element is a stable modification of the mitc4 element we report on calculations with this new element the original mitc4 and also the bilinear element with selective reduced integration the numerical results are in accordance with the results of the numerical analysis and they show that i the method with reduced integration is highly unreliable and cannot be recommended ii the mitc4 performs rather well but its instability can lead to a decrease in accuracy for the deflection and especially to an inaccurate and oscillating shear force iii the drawbacks of the mitc4 are not present in the modified method

a note on the design of hp adaptive finite element methods for elliptic partial differential equations we introduce an hp adaptive finite element algorithm based on a combination of reliable and efficient residual error indicators and a new hp extension control technique which assesses the local regularity of the underlying analytical solution on the basis of its local legendre series expansion numerical experiments confirm the robustness and reliability of the proposed algorithm

simulation of a free boundary problem using boundary element method and restarted re analysis technique in this work we deal with the numerical approximation of a free boundary problem reformulated as an optimal shape design one the boundary element method is used for the approximation of this problem the iterative method used to solve the discrete problem requires the resolution of intermediate linear systems associated with the successive modification in the design process in many cases one of the main obstacles is the high computational cost involved in the solution of large scale problems to reduce the computational cost a restarted re analysis technique is introduced to solve these systems numerical examples including comparison results are presented to show the efficiency of the proposed approach

numerical analysis of graded mesh methods for a class of second kind integral equations on the real line abstract in this paper we are concerned with the numerical analysis of the collocation method based on graded meshes of second kind integral equations on the real line of the form s s r s t z t t dt s r where l 1 r z l r and bc r the space of bounded continuous complex valued functions on r are assumed known and the function bc r is to be determined we introduce some new graded meshes for the collocation method of the integral equation which are different from those used previously for the wiener hopf integral equation in the case when the solution decays exponentially at infinity and establish optimal local and global l norm error estimates under the condition that the solution decays only polynomially at infinity

finite dimensional approximation of bifurcation problems in presence of symmetries we give here a brief summary of the results of 4 14 the aim of our work was not only the finite dimensional approximation of the specific problem studied in 3 but we also wanted to show how to adapt to discrete problems and how to use in this case some classical mathematical tools e g the splitting lemma of gromoll meyer magnus the singularity theory etc such considerations are developed in 5 in particular we prove in 5 that in most cases e g in the examples given in 6 7 9 10 the discrete bifurcation problem behaves as an imperfect bifurcation problem and we improve the methods of 12 another way to use universal unfoldings in the approxima tion of bifurcation problems is suggested by 2

strongly elliptic boundary integral equations for electromagnetic transmission problems we study a boundary integral equation method for transmission problems for strongly elliptic differential operators which yields a strongly elliptic system of pseudodifferential operators and which therefore can be used for numerical computations with galerkin s procedure the method is shown to work for the vector helmholtz equation in 3 with electromagnetic transmission conditions we propose a slightly modified system of boundary values in order for the corresponding bilinear form to be coercive over h 1 we analyse the boundary integral equations using the calculus of pseudodifferential operators here the concept of the principal symbol is used to derive existence and regularity results for the solution

on principles for the selection of shape functions for the generalized finite element method abstract effective shape functions for the generalized finite element method should reflect the available information on the solution this information is partially fuzzy because the solution is of course unknown and typically the only available information is the solution s inclusion in a variety of function spaces it is desirable to choose shape functions that perform robustly over a family of relevant situations quantitative notions of robustness are introduced and discussed we show in particular that in one dimension polynomials are robust when the available information consists in inclusions in sobolev type spaces that are x independent

the extended domain eigenfunction method for solving elliptic boundary value problems with annular domains standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely if ever obtainable in this paper we propose a solution technique wherein we embed the original

the efficient implementation of a finite element multi resolution viscosity method for hyperbolic conservation laws it is well known that the classic galerkin finite element method is unstable when applied to hyperbolic conservation laws such as the euler equations for compressible flows adding a diffusion term to the equations stabilizes the method but sacrifices too much accuracy to be of any practical use an elegant solution developed in the context of spectral methods by eitan tadmor and coworkers is to add diffusion only to the high frequency modes of the solution and can lead to stabilization without sacrificing accuracy we incorporate this idea into the finite element framework by using hierarchical functions as a multi frequency basis the result is a new finite element method for solving hyperbolic conservation laws for this method convergence for a one dimensional scalar conservation law has previously been proved here the method is described in detail several issues connected with its efficient implementation are considered and numerical results for several examples involving one and two dimensional hyperbolic conservation laws are provided several advantageous features of the method are discussed including the ease for which discontinuities can be detected and artificial diffusion can be applied anisotropically and locally in physical as well as frequency space

modeling of convection dominated thermoporomechanics problems using incomplete interior penalty galerkin method abstract in order to obtain converged and accurate numerical solutions in general small time steps are required for time dependent problems for popular continuous finite elements however the use of small time steps often results in oscillatory pressures and temperatures for thermoporomechanics problems with low conductivities moreover convection dominated thermal poromechanics problems often have very sharp temperature fronts that propagate over spatial domains when applied to these problems continuous elements present serious deficiencies in that large error induced in coarse mesh zones will propagate and pollute the solutions in fine mesh zones such oscillatory and polluted solutions are nonphysical and must be precluded we propose discontinuous galerkin methods to be alternatives to handle these challenges this paper focuses on the finite element formulation of the incomplete interior penalty galerkin method on thermoporoelasticity problems with heat convection in this formulation we propose discontinuous spaces for all three field variables to deal with the convection effect an upwinding scheme is simply and elegantly implemented through element interfaces which is favored by the discontinuous galerkin framework in addition the inner pressure boundary conditions important to many engineering problems are also taken into account in our discontinuous galerkin formulation excellent performance of this discontinuous galerkin method on precluding temperature oscillations and on blocking error propagation is demonstrated through solving a convection dominated oil well injection problem

on the geodesic form of second order dynamic equations it is shown that any second order dynamic equation on a configuration bundle q r of nonrelativistic mechanics is equivalent to a geodesic equation with respect to a nonlinear connection on the tangent bundle tq q the case of quadratic dynamic equations is analyzed in detail the equation for jacobi vector fields is constructed and investigated by the geometric methods

numerical methods for treating problems of viscoelastic isotropic solid deformation mathematical models for treating problems of linear viscoelasticity involving hereditary constitutive relations for compressible solids are discussed and their discretization using finite element methods in space together with quadrature rules in time to treat the hereditary integrals is described the range of applicability of this type of formulation is reviewed in the context of geometric and constitutive linearity nonlinearity and the limitations imposed by the availability of physical data are discussed one of the above models is a volterra integral equation of the second kind in this when the kernel is separable an established technique due to goursat 1933 can be exploited to reformulate the problem as a system of ordinary differential equations this approach will be described for the special case of a linear viscoelastic isotropic homogeneous synchronous constant poisson s ratio solid this method results in a complete decoupling of the space and time dependence in this case the problem can be solved at each time level by solving first a problem of linear elasticity and then a system of ordinary differential equations for each point in the spatial mesh at which the viscoelastic displacements are required the advantages disadvantages and limitations offered by this and various other schemes for solving problems of viscoelasticity as outlined below are discussed

a posteriori error estimates for space time finite element approximation of quasistatic hereditary linear viscoelasticity problems abstract we give a space time galerkin finite element discretisation of the quasistatic compressible linear viscoelasticity problem as described by an elliptic partial differential equation with a fading memory volterra integral the numerical scheme consists of a continuous galerkin approximation in space based on piecewise polynomials of degree p 0 cg p with a discontinuous galerkin piecewise constant dg 0 or linear dg 1 approximation in time a posteriori galerkin error estimates are derived by exploiting the galerkin framework and optimal stability estimates for a related dual backward problem the a posteriori error estimates are quite flexible strong lp energy norms of the errors are estimated using time derivatives of the residual terms when the data are smooth while weak energy norms are used when the data are non smooth in time we also give upper bounds on the dg 0 cg 1 a posteriori error estimates which indicate optimality however a complete analysis is not given

a second order characteristics finite element scheme for natural convection problems in this paper a second order characteristics finite element scheme is applied to the numerical solution of natural convection problems firstly after recalling the mathematical model a second order time discretization of the material time derivative is introduced next fully discretized schemes are proposed by using finite element methods numerical results for the two dimensional problem of buoyancy driven flow in a square cavity with differentially heated side walls are given and compared with a reference solution

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

toward approximate moving least squares approximation with irregularly spaced centers abstract by combining the well known moving least squares approximation method and the theory of approximate approximations due to maz ya and schmidt we are able to present an approximate moving least squares method which inherits the simplicity of shepard s method along with the accuracy of higher order moving least squares approximations in this paper we focus our interest on practical implementations for irregularly spaced data sites the two schemes described here along with some first numerical experiments are to be viewed as exploratory work only these schemes apply to centers that are obtained from gridded centers via a smooth parametrization further work to find a robust numerical scheme applicable to arbitrary scattered data is needed

analytical solutions for the incompressible viscous flow within a rectangular domain abstract analytical solutions of the velocity pressure and stream function are developed for the slow incompressible viscous fluid in a simple rectangular domain all solutions can be applied to the boundary integral techniques as typical fundamental solutions

an eulerian method for transient nonlinear free surface wave problems abstract an eulerian difference method is developed for the transient potential flow of an incompressible fluid with fully nonlinear free surface conditions the free surface coordinate y x t and the velocity potential x y t on the free surface are recognized as the primary unknowns to be solved as an initial value problem from the pair of nonlinear partial differential equations representing the dynamic and the kinematic conditions of the free surface the continuity relation 2 0 for the velocity potential x y t over the flow field below the free surface is recognized as a subsidiary condition to be enforced at all times the field of computation is transformed into a time invariant cartesian region with the free surface x t represented by a coordinate line or surface the iterative solution for x y t p x y t in this fixed field of computation is facilitated by the use of fast fourier transform fft the iterative process converges rapidly in terms of this converged x y t the free surface location x t and its potential x y t are advanced in time results from two planar examples are illustrated the method is equally applicable to problems in three space dimensions possibly involving interactive matching with neighboring flow fields if the initial free surface potential x y t 0 is unknown difficulties may be encountered in data specification for securing a well posed problem for solution

critical friction for wedged configurations abstract a wedged configuration with coulomb friction is a nontrivial equilibrium state of a linear elastic body in a frictional unilateral contact with a rigid body under vanishing external loads we analyze here the relation between the geometry of the elastic body and the friction coefficient for which wedged configurations exist in a 3 d context the critical friction coefficient w is defined as the infimum of a supremal functional defined on the set of admissible normal displacement and tangential stresses for friction coefficients with w the wedged problem has at least a solution and for the wedged problem is stated in a discrete framework using a mixed finite element approach and the discrete critical friction coefficient h w is introduced as the solution of a global minimization problem involving a non differentiable and non convex functional the existence of h the displacement field of a critical wedged state is proved and a specific numerical method based on a genetic algorithm was developed to compute the critical wedged configurations some techniques to handle the discontinuities of the normal vector on the contact surface are presented and the analysis is illustrated with three numerical simulations

on some recent adventures into improved finite element cfd methods for convective transport abstract the quest continues for computational fluid dynamics cfd algorithms that are accurate and efficient for convection dominated applications including shocks travelling fronts and wall layers the boundary value optimal galerkin weak statement invariably requires manipulation either in the test space or in an augmented form for the conservation law system to handle the disruptive character introduced by the discretized first order convection term an incredible variety of methodologies have been derived and examined to address this issue in particular seeking achievement of accurate and monotone discrete approximate solutions in an efficient implementation the utk cfd research group continues its search on examining the breadth of approaches leading to development of a consistent encompassing theoretical statement exhibiting quality performance included herein are adventures into generalized taylor series lax wendroff methods characteristic euler flux resolutions sub grid embedded high degree lagrange bases with static condensation and assembled stencil fourier analysis optimization for finite element weak statement implementations for appropriate model problems including steady convection diffusion and pure unsteady convection and benchmark navier stokes definitions recent advances have lead to candidate accurate monotone methods with linear basis efficiency this contribution highlights the theoretical developments and presents quantitative documentation of achievable high quality solutions

a velocity stream function method for three dimensional incompressible fluid flow abstract we describe a velocity stream function method for computing incompressible fluid flow extending earlier work in two to three dimensions we present a strictly divergence free finite element in primitive variables in 3d as the curl of a generalized hermite vector potential element with velocity degrees of freedom and show a method for its derivation this linear velocity element is defined on a reference cube with 8 nodes each node having 3 vector potential stream function and 3 velocity degrees of freedom the method and element are applied to the lid driven cavity problem and open duct flow in three dimensions

interior superconvergence in mortar and non mortar mixed finite element methods on non matching grids we establish interior velocity superconvergence estimates for mixed finite element approximations of second order elliptic problems on non matching rectangular and quadrilateral grids both mortar and non mortar methods for imposing the interface conditions are considered in both cases it is shown that a discrete l 2 error in the velocity in a compactly contained subdomain away from the interfaces con1 2 higher than the error in the whole domain for the non mortar method we also establish pressure superconvergence which is needed in the velocity analysis numerical results are presented in confirmation of the theory

absolute continuity of symmetric diffusions let x and y be symmetric diffusion processes with a common state space and let p m resp q be the law of x resp y with its symmetry measure m resp as initial distribution we study the consequences of the absolute continuity condition q t 1 t the density p also serves to link the dirichlet forms of x and y in a simple way our identification of l relies on notions of even and odd for additive functionals these notions complement fukushima s decomposition and the forward backward martingale decomposition of lyons and zheng

a priori and a posteriori error analysis for a large scale ocean circulation finite element model we consider the finite element solution of the stream function vorticity formulation for a large scale ocean circulation model first we study existence and uniqueness of solution for the continuous and discrete problems under appropriate regularity assumptions we prove that the stream function can be computed with an error of order h in h1 seminorm second we introduce and analyze an h adaptive mesh refinement strategy to reduce the spurious oscillations and poor resolution which arise when convective terms are dominant we propose an a posteriori anisotropic error indicator based on the recovery of the hessian from the finite element solution which allows us to obtain well adapted meshes the numerical experiments show an optimal order of convergence of the adaptive scheme furthermore this strategy is efficient to eliminate the oscillations around the boundary layer

equilibrium subsets for multi parametric structural analysis the paper discusses multi parametric formulations for structural equilibrium problems by seeking subsets of equilibrium states which also fulfil extra conditions more detailed information on structural behaviour can be obtained these conditions can be related to analyses of e g critical behaviour imperfections or optimisation the paper shows a general problem setting and some interesting augmentations a solution method for the special case of one dimensional equilibrium subsets is described the algorithm is a generalisation of a path following algorithm where new methods are developed for the evaluation of the path tangent and for the isolation of special solution points examples are used to show the properties and the possibilities of the ideas

multilevel methods for the h p and hp versions of the boundary element method in this paper we give an overview on the definition of finite element spaces for the h p and hp version of the bem along with preconditioners of additive schwarz type we consider screen problems with a hypersingular or a weakly singular integral equation of first kind on an open surface as model problems for the hypersingular integral equation and the h version with piecewise bilinear functions on a coarse and a fine grid we analyze a preconditioner by iterative substructuring based on a non overlapping decomposition of we prove that the condition number of the preconditioned linear system behaves polylogarithmically in h h here h is the size of the subdomains and h is the size of the elements for the hp version and the hypersingular integral equation we comment in detail on an additive schwarz preconditioner which uses piecewise polynomials of high degree on the fine grid and yields also a polylogarithmically growing condition number for the weakly singular integral equation where no continuity of test and trial functions across the element boundaries has to been enforced the method works for nonuniform degree distributions as well numerical results supporting our theory are reported

parallel galerkin domain decomposition procedures based on the streamline diffusion method for convection diffusion problems based upon the streamline diffusion method parallel galerkin domain decomposition procedures for convection diffusion problems are given these procedures use implicit method in the sub domains and simple explicit flux calculations on the inter boundaries of sub domains by integral mean method or extrapolation method to predict the inner boundary conditions thus the parallelism can be achieved by these procedures the explicit nature of the flux calculations induces a time step limitation that is necessary to preserve stability artificial diffusion parameters d are given by analysis optimal order error estimate is derived in a norm which is stronger than l 2 norm for these procedures this error estimate not only includes the optimal h 1 norm error estimate but also includes the error estimate along the streamline direction b u u which cannot be achieved by standard finite element method experimental results are presented to confirm theoretical results

error controlled global sensitivity analysis of ordinary differential equations we propose a novel strategy for global sensitivity analysis of ordinary differential equations it is based on an error controlled solution of the partial differential equation pde that describes the evolution of the probability density function associated with the input uncertainty variability the density yields a more accurate estimate of the output uncertainty variability where not only some observables such as mean and variance but also structural properties e g skewness heavy tails bi modality can be resolved up to a selected accuracy for the adaptive solution of the pde cauchy problem we use the rothe method with multiplicative error correction which was originally developed for the solution of parabolic pdes we show that unlike in parabolic problems conservation properties necessitate a coupling of temporal and spatial accuracy to avoid accumulation of spatial approximation errors over time we provide convergence conditions for the numerical scheme and suggest an implementation using approximate approximations for spatial discretization to efficiently resolve the coupling of temporal and spatial accuracy the performance of the method is studied by means of low dimensional case studies the favorable properties of the spatial discretization technique suggest that this may be the starting point for an error controlled sensitivity analysis in higher dimensions

parallel domain decomposition procedures of improved d d type for parabolic problems two parallel domain decomposition procedures for solving initial boundary value problems of parabolic partial differential equations are proposed one is the extended d d type algorithm which extends the explicit implicit conservative galerkin domain decomposition procedures given in 5 from a rectangle domain and its decomposition that consisted of a stripe of sub rectangles into a general domain and its general decomposition with a net like structure an almost optimal error estimate without the factor h 1 2 given in dawson dupont s error estimate is proved another is the parallel domain decomposition algorithm of improved d d type in which an additional term is introduced to produce an approximation of an optimal error accuracy in l 2 norm

fem bem coupling for the large body limit in micromagnetics we present and analyze a coupled finite element boundary element method for a model in stationary micromagnetics the finite element part is based on mixed conforming elements for two and three dimensional settings we show well posedness of the discrete problem and present an a priori error analysis for the case of lowest order elements

the conditioning of some numerical methods for first kind boundary integral equations we consider the sensitivity of the matrix equations which arise when solving boundary integral equations of negative order specifically in case of the typical example of the operator with logarithmic kernel the sensitivity is expressed using condition numbers and it turns out that the local condition number is a very good indicator in contrast to the ordinary condition number traditionally used

hamiltonian time dependent mechanics the usual formulation of time dependent mechanics implies a given splitting y r m of an event space y this splitting however is broken by any time dependent transformation including transformations between inertial frames the goal is the frame covariant formulation of time dependent mechanics on a bundle y r whose fibration y m is not fixed its phase space is the vertical cotangent bundle v y provided with the canonical 3 form and the corresponding canonical poisson structure an event space of relativistic mechanics is a manifold z whose fibration z r is not fixed

enhanced allman quadrilateral for finite drilling rotations the paper concerns a four node quadrilateral element based on allman shape functions undergoing finite unrestricted drilling rotations and aims at improving its accuracy and facilitating its implementation firstly the classical allman shape functions are valid only for small in plane rotations and must be used with a co rotational frame which embeds finite rotations we derive a new form of allman shape functions which is valid for finite drilling rotations and allows to avoid the use of such a frame secondly the classical allman quadrilateral shows locking in the in plane shear test we study this problem identify its source and remove it by enhancing the element with two additional modes via the enhanced assumed displacement gradient eadg method to accomplish this we extend the original version of the method to mixed functionals including rotations two variational formulations including the drilling rotation via the rotation constraint rc equation are considered one based on the green strain and the other on the relaxed non symmetric right stretch strain numerical tests of the corresponding finite elements show that the improved allman elements are as exact in linear tests as the eadg4 element and perform very well in a severe in plane shear test for one layer of elements undergoing large rotations

on the equivalence of three potential principles for right markov processes we examine three of the principles of probabilistic potential theory in a nonclassical setting these are i the bounded maximum principle ii the positive definiteness of the energy of measures of bounded potential and iii the condition that each semipolar set is polar these principles are known to be equivalent in the context of two markov processes in strong duality when excessive functions are lower semicontinuous we show that when the principles are appropriately formulated their equivalence persists in the wider context of a borel right markov processx with distinguished excessive measurem we make no duality hypotheses andm need not be a reference measure our main tools are the stationary process y qm associated withx andm and a correspondence between potentials u and certain random measures over y qm

on the fem solution of a coupled contact two phase stefan problem in thermo elasticity coercive case abstract in the paper a semi implicit discretization in time of the weak formulation of the coupled signorini type contact two phase stefan problem is numerically analyzed the problem leads to coupled elliptic variational inequalities which are approximated by the fem

full order convergence of a mixed finite element method for fourth order elliptic equations abstract by using a special interpolation operator and an elaborate element analysis in this paper we improve the classical error estimates to full order for a mixed finite element method for the fourth order elliptic equations on the rectangular mesh therefore we obtain the truly optimal error estimates in view of the interpolation space for the first time

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

domain decomposition based mathcal h lu preconditioning hierarchical matrices provide a data sparse way to approximate fully populated matrices the two basic steps in the construction of an mathcal h matrix are a the hierarchical construction of a matrix block partition and b the blockwise approximation of matrix data by low rank matrices in this paper we develop a new approach to construct the necessary partition based on domain decomposition compared to standard geometric bisection based mathcal h matrices this new approach yields mathcal h lu factorizations of finite element stiffness matrices with significantly improved storage and computational complexity requirements these rigorously proven and numerically verified improvements result from an mathcal h matrix block structure which is naturally suited for parallelization and in which large subblocks of the stiffness matrix remain zero in an lu factorization we provide numerical results in which a domain decomposition based mathcal h lu factorization is used as a preconditioner in the iterative solution of the discrete three dimensional convection diffusion equation

non standard connections in classical mechanics in the jet bundle description of first order classical field theories there are some elements such as the lagrangian energy and the construction of the hamiltonian formalism which require the prior choice of a connection bearing these facts in mind we analyse the situation in the jet bundle description of time dependent classical mechanics we prove that this connection dependence also occurs in this case although it is usually hidden by the use of the natural connection given by the trivial bundle structure of the phase spaces under consideration however we also prove that this dependence is dynamically irrelevant except where the dynamical variation of the energy is concerned in addition the relationship between first integrals and connections is shown for a sufficiently large class of lagrangians

parallel galerkin domain decomposition procedures for wave equation parallel galerkin domain decomposition procedures for wave equation are given these procedures use implicit method in the sub domains and simple explicit flux calculation on the inter boundaries of sub domains by integral mean method or extrapolation method thus the parallelism can be achieved by these procedures the explicit nature of the flux prediction induces a time step constraint that is necessary to preserve the stability l 2 norm error estimates are derived for these procedures experimental results are presented to confirm the theoretical results

a locking free reissner mindlin quadrilateral element on arbitrary regular quadrilaterals a new finite element method for the reissner mindlin plate is proposed where both transverse displacement and rotation are approximated by isoparametric bilinear elements with local bubbles enriching rotation and a local reduction operator is applied to the shear energy term this new method gives optimal error bounds uniform in the thickness of the plate for both transverse displacement and rotation with respect to h1 and l2 norms

a non mortar mixed finite element method for elliptic problems on non matching multiblock grids abstract we consider the approximation of second order elliptic equations on domains that can be described as a union of sub domains or blocks we assume that a grid is defined on each block independently so that the resulting grid over the entire domain need not be conforming i e match across the block boundaries several techniques have been developed to approximate elliptic equations on multiblock grids that utilize a mortar finite element space defined on the block boundary interface itself we define a mixed finite element method that does not use such a mortar space the method has an advantage in the case where adaptive local refinement techniques will be used in that there is no mortar grid to refine as is typical of mixed methods our method is locally conservative element by element it is also globally conservative across the block boundaries theoretical results show that the approximate solution converges at the optimal rate to the true solution we present computational results to illustrate and confirm the theory

on two dimensional slow viscous flows past obstacles in a half plane we consider a cylinder with arbitrary cross section moving in a viscous incompressible fluid parallel to a plane wall formal asymptotic expansions of the solution for small reynolds numbers are constructed by using boundary integral equations of the first kind in contrast to the problem without a wall we show that there exists a unique solution to the zero th order problem however the problem considered here is still singular in the sense that we find the stokes paradox in the next higher order problem a justification of the formal asymptotic expansion for the first two terms is established rigorously

jet methods in nonholonomic mechanics classical nonholonomic mechanical systems are studied whose evolution space is a fiber bundle m r the framework is that of jet spaces in which the geometrical meaning of the theory emerges clearly for systems with linear constraints a new interpretation is given of appell s equations as first order differential equations associated with a suitable vector field the d alembert principle is formulated in an appropriate way to be generalized to systems with nonlinear constraints the equivalence between the equations of motion arising from this generalization the ones set up on gauss principle of least constraint and hertz s principle of least curvature is established

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

a mixed finite element method and solution multiplicity for coulomb frictional contact abstract this paper is concerned with the discrete contact problem governed by coulomb s friction law we propose and study a new technique using mixed finite elements with two multipliers in order to determine numerically critical friction coefficients for which multiple solutions to the friction problem exist the framework is based on eigenvalue problems and it allows to exhibit non uniqueness cases involving an infinity of solutions located on a continuous branch the theory is illustrated with several computations which clearly show the accuracy of the proposed method

homogeneous random measures and a weak order for the excessive measures of a markov process let x xt px be a right markov process and let m be an excessive measure for x associated with the pair x m is a stationary strong markov process yt qm with random times of birth and death with the same transition function as x and with m as one dimensional di stribution we use yt qm to study the cone of excessive measures for x a weak order is defined on this cone an excessive measure is weakly dominated by m if and only if there is a suitable homogeneous random measure tt such that yt q6 is obtained by birthing yt qm birth in t t dt occurring at rate s dt random measures such as s are studied through the use of palm measures we also develop aspects of the general theory of processes over yt qm including the moderate markov property of yt qm when the arrow of time is reversed applications to balayage and capacity are suggested

nonholonomic constraints in time dependent mechanics the constraint reaction force of ideal nonholonomic constraints in time dependent mechanics on a configuration bundle q r is obtained using the vertical extension of hamiltonian formalism to the vertical tangent bundle vq of q r the hamiltonian of a nonholonomic constrained system is constructed the present setting is more general than the one usually considered in the literature on nonholonomic mechanics