high order methods for low reynolds number flows around moving obstacles based on universal meshes summary we propose a family of methods for simulating two dimensional incompressible low reynolds number flow around a moving obstacle whose motion is prescribed the methods make use of a universal mesh a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle s boundary the resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off the shelf time integrators we demonstrate the approach by using taylor hood elements to approximate the fluid velocity and pressure to integrate in time we consider implicit runge kutta schemes as well as a fractional step scheme we illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations copyright 2015 john wiley sons ltd

local projection stabilization for the oseen problem and its interpretation as a variational multiscale method we propose to apply the recently introduced local projection stabilization to the numerical computation of the oseen equation at high reynolds number the discretization is done by nested finite element spaces using a priori error estimation techniques we prove the convergence of the method the a priori estimates are independent of the local peclet number and give a sufficient condition for the size of the stabilization parameters in order to ensure optimality of the approximation when the exact solution is smooth moreover we show how this method may be cast in the framework of variational multiscale methods we indicate what modeling assumptions must be made to use the method for large eddy simulations

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

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

on the minimum distance conjecture for schubert codes in 2000 s r ghorpade and g lachaud presented a conjecture on the minimum distance of algebraic geometric codes associated to schubert varieties in this correspondence we use the structure and properties of the exterior algebra to give an elementary proof of this conjecture and provide a construction of codewords of minimum hamming weight

geometric hyperplanes of embeddable grassmannians abstract it is proved that every geometric hyperplane of an embeddable grassmann space of finite rank arises from an embedding an equivalent formulation of this result amounts to a geometric characterization of alternating k linear forms

pressure stability in fractional step finite element methods for incompressible flows abstract the objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure poisson equation for the classical first order projection method it is shown that there is a pressure control which depends on the time step size and therefore there is a lower bound for this time step for stability reasons the situation is much worse for a second order scheme in which part of the pressure gradient is kept in the momentum equation the pressure stability in this case is extremely weak to overcome these shortcomings a stabilized fractional step finite element method is also considered and its stability is analyzed some simple numerical examples are presented to support the theoretical results

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

an arbitrary lagrangian eulerian formulation for a 3d eutrophication model in a moving domain this work analyzes a realistic mathematical model that governs eutrophication an ecological process involving nutrients phytoplankton zooplankton organic detritus and dissolved oxygen into a moving aquatic domain as a main result we obtain existence uniqueness results for the solution of the system within the general framework of non cylindrical domains based on studying the properties of a generic parabolic problem the fact of dealing with moving domains and the lack of regularity preclude the use of standard semigroup approach forcing us towards the utilization of arbitrary lagrangian eulerian techniques

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

on the legendre map in higher order field theories the authors show how the construction of a cartan form in higher order field theories defines a legendre map and how the regularity of this map may be described in terms of a sequence of maps between intermediate phase spaces they also show how semi holonomic jets are important in this context they allow the definition of regularity to be applied without ambiguity to the lagrangian itself and they permit the specification of a unique cartan form legendre map and covariant phase space for second order lagrangians

analysis of a fluid structure interaction problem recast in an optimal control setting fluid structure interaction fsi simulation presents many computational difficulties particularly when the densities of the fluid and structure are close a previous report p kuberry and h lee comput methods appl mech engrg 267 2013 pp 594 605 has suggested that recasting the fsi problem in the context of optimal control may significantly reduce computation time this paper introduces a neumann type control along with detailed analysis for the stability and existence of an optimal solution for a given time step the existence of lagrange multipliers is proved and an optimality system is derived a gradient based optimization algorithm is then presented with numerical results confirming its effectiveness in computing an accurate solution

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

an l stability analysis for the finite difference solution of one dimensional linear convection diffusion equations on moving meshes the stability of three moving mesh finite difference schemes is studied in the l norm for one dimensional linear convection diffusion equations these schemes use central finite differences for spatial discretization and the q method for temporal discretization and they are based on conservative and non conservative forms of transformed partial differential equations the stability conditions obtained consist of the cfl condition and the mesh speed related conditions the cfl condition is independent of the mesh speed and has the same form as that for fixed meshes the mesh speed related conditions restrict how fast the mesh can move the conditions of this type obtained in this paper are weaker than those in the existing literature and can be satisfied when the mesh is sufficiently fine illustrative numerical results are presented

the structure of dual schubert union codes in this paper we prove that schubert union codes are tanner codes constructed from the point line incidence geometry inherited from the grassmannian our proof is based on an iterative encoding algorithm for tanner codes this encoder determines the entries of a code word of a tanner code from the entries in a given subset of its positions as a result we find sufficient conditions on the initial positions such that a code word is determined from the component codes only this algorithm has linear complexity in the code length we also use this encoder to determine the minimum distance of schubert union codes in terms of the minimum distance of the schubert varieties contained therein

ale supg finite element method for convection diffusion problems in time dependent domains conservative form a streamline upwind petrov galerkin supg finite element method for a convection dominated transient convection diffusion reaction equation in time dependent domains is proposed the time dependent domain is handled by the arbitrary lagrangian eulerian ale approach whereas the supg method is used for the spatial discretization further the first order modified backward euler and the second order modified crank nicolson methods are used for the temporal discretization it is shown that the stability of the semi discrete continuous in time conservative ale supg equation is independent of the mesh velocity whereas the stability of the fully discrete scheme with the implicit euler time discretization is unconditionally stable and is only conditionally stable time step depends on mesh velocity with the crank nicolson method numerical results are presented to support the stability estimates and to show the influence of the supg stabilization parameter in a time dependent domain further the proposed numerical scheme is applied to a boundary layer problem in a time dependent domain c 2017 elsevier inc all rights reserved

finite element error estimation for quasi newtonian fluid structure interaction problems we consider a monolithic scheme for fluid structure interaction problems involving an incompressible quasi newtonian fluid the monolithic formulation is obtained using the arbitrary lagrangian eulerian ale method with matching conditions at the fluid structure interface the stability and error analysis are performed for the finite element approximation finally some numerical experiments that confirm the theoretical analysis are presented

on the extraction of the boundary conditions and the boundary ports in second order field theories in this paper we consider second order field theories in a variational setting from the variational principle the euler lagrange equations follow in an unambiguous way but it is well known that this is not true for the cartan form this also has consequences on the derivation of the boundary conditions when non trivial variations are allowed on the boundary by posing extra conditions on the set of possible boundary terms we exploit the degree of freedom in the cartan form to extract physical meaningful boundary expressions the same mathematical machinery will be applied to derive the boundary ports in a hamiltonian representation of the partial differential equations which is crucial for energy based control approaches our results will be visualized for mechanical systems such as beam and plate models in this paper we consider second order field theories in a variational setting from the variational principle the euler lagrange equations follow in an unambiguous way but it is well known that this is not true for the cartan form this also has consequences on the derivation of the boundary conditions when non trivial variations are allowed on the boundary by posing extra conditions on the set of possible boundary terms we exploit the degree of freedom in the cartan form to extract physical meaningful boundary expressions the same mathematical machinery will be applied to derive the boundary ports in a hamiltonian representation of the partial differential equations which is crucial for energy based control approaches our results will be visualized for mechanical systems such as beam and plate models

parametric fem for geometric biomembranes we consider geometric biomembranes governed by an l 2 gradient flow for bending energy subject to area and volume constraints helfrich model we give a concise derivation of a novel vector formulation based on shape differential calculus and corresponding discretization via parametric fem using quadratic isoparametric elements and a semi implicit euler method we document the performance of the new parametric fem with a number of simulations leading to dumbbell red blood cell and toroidal equilibrium shapes while exhibiting large deformations

finite element discretization of the navier stokes equations with a free capillary surface the instationary navier stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions a stable finite element discretization is presented the key idea is the treatment of the curvature terms by a variational formulation in the context of a discontinuous in time space time element discretization stability in weak energy norms can be proved numerical examples in 2 and 3 space dimensions are given

second order time accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes abstract we consider the solution of two and three dimensional flow problems with moving boundaries using the arbitrary lagrangian eulerian formulation or dynamic meshes we focus on the case where spatial discretization is performed by unstructured finite volumes and or finite elements we formulate the consequence of the geometric conservation law on the second order implicit temporal discretization of the semi discrete equations governing such problems and use it as a guideline to construct a new family of second order time accurate and geometrically conservative implicit numerical schemes for flow computations on moving grids we apply these new algorithms to the solution of three dimensional flow problems with moving and deforming boundaries demonstrate their superior accuracy and computational efficiency and highlight their impact on the simulation of fluid structure interaction problems

on the minimum distances of schubert codes ghorpade and lachaud 1998 introduced schubert codes as codes corresponding to the protective system tsfasman and vladut 1991 defined by schubert subvarieties of grassmann varieties gr l m they gave an upper bound for the minimum distances of these codes in ghorpade and lachaud and conjectured their true minimum distances in this note we prove the conjecture in the case of l 2

time discrete higher order ale formulations stability arbitrary lagrangian eulerian ale formulations deal with pdes on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity this arbitrary extension has no effect on the stability of the pde but may influence that of a discrete scheme we examine this critical issue for higher order time stepping without space discretization we propose time discrete discontinuous galerkin dg numerical schemes of any order for a time dependent advection diffusion model problem in moving domains and study their stability properties the analysis hinges on the validity of the reynolds identity for dg exploiting the variational structure and assuming exact integration we prove that our conservative and nonconservative dg schemes are equivalent and unconditionally stable the same results remain true for piecewise polynomial ale maps of any degree and suitable quadrature that guarantees the validity of the reynolds identity this approach general

a θ stable approximations of abstract cauchy problems we study the approximation of linear parabolic cauchy problems by means of galerkin methods in space anda stable multistep schemes of arbitrary order in time the error is evaluated in the norm ofl t 2 h x 1 l t l x 2

constrained variational calculus for higher order classical field theories we develop an intrinsic geometrical setting for higher order constrained field theories as a main tool we use an appropriate generalization of the classical skinner rusk formalism some examples of applications are studied in particular to the geometrical description of optimal control theory for partial differential equations

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

stability convergence and accuracy of stabilized finite element methods for the wave equation in mixed form in this paper we propose two stabilized finite element methods for different functional frameworks of the wave equation in mixed form these stabilized finite element methods are stable for any pair of interpolation spaces of the unknowns the variational forms corresponding to different functional settings are treated in a unified manner through the introduction of length scales related to the unknowns stability and convergence analysis is performed together with numerical experiments it is shown that modifying the length scales allows one to mimic at the discrete level the different functional settings of the continuous problem and influence the stability and accuracy of the resulting methods

modeling cell movement and chemotaxis using pseudopod based feedback a computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis an empirical pattern formation model based on a system of nonlinear reaction diffusion equations is approximated on an evolving cell boundary using an arbitrary lagrangian eulerian surface finite element method ale sfem the solution state is used to drive a mechanical model of the protrusive and retractive forces exerted on the cell boundary movement of the cell is achieved using a level set method results are presented for cell migration with and without chemotaxis the simulated behavior is compared with experimental results of migrating dictyostelium discoideum cells

numerical methods for hamiltonian pdes the paper provides an introduction and survey of conservative discretization methods for hamiltonian partial differential equations the emphasis is on variational symplectic and multi symplectic methods the derivation of methods as well as some of their fundamental geometric properties are discussed basic principles are illustrated by means of examples from wave and fluid dynamics

a high order splitting method for time dependent domains abstract we present a temporal splitting scheme for the semi discrete convection diffusion equation and the semi discrete incompressible navier stokes equations in time dependent geometries the proposed splitting scheme can be considered as an extension of the oif method proposed in maday et al y maday a t patera e m ronquist an operator integration factor splitting method for time dependent problems application to incompressible fluid flow j sci comput 5 4 1990 263 292 in the sense that it can be interpreted as a semi lagrangian method for time dependent domains the semi discrete equations are derived from an arbitrary lagrangian eulerian ale formulation of the governing equations and are discretized in space using high order spectral elements the proposed splitting scheme has been tested numerically on model problems with known analytical solutions and first second and third order convergence in time has been obtained we also show that it is not necessary for the interior mesh velocity to be obtained through the use of an elliptic solver numerical tests show that it is sufficient that the mesh velocity is regular within each spectral element and only c 0 continuous across element boundaries this is consistent with the theoretical results presented in formaggia and nobile l formaggia f nobile a stability analysis for the arbitrary lagrangian eulerian formulation with finite elements east west j numer math 7 2 1999 105 131 in addition the mesh velocity should be regular in the time direction

time discrete higher order ale formulations a priori error analysis we derive optimal a priori error estimates for discontinuous galerkin dg time discrete schemes of any order applied to an advection diffusion model defined on moving domains and written in the arbitrary lagrangian eulerian ale framework our estimates hold without any restrictions on the time steps for dg with exact integration or reynolds quadrature they involve a mild restriction on the time steps for the practical runge kutta radau methods of any order the key ingredients are the stability results shown earlier in bonito et al time discrete higher order ale formulations stability 2013 along with a novel ale projection numerical experiments illustrate and complement our theoretical results

time dependent subscales in the stabilized finite element approximation of incompressible flow problems abstract in this paper we analyze a stabilized finite element approximation for the incompressible navier stokes equations based on the subgrid scale concept the essential point is that we explore the properties of the discrete formulation that results allowing the subgrid scales to depend on time this apparently natural idea avoids several inconsistencies of previous formulations and also opens the door to generalizations

a posteriori error estimation for the steady navier stokes equations in random domains we consider finite element error approximations of the steady incompressible navier stokes equations defined on a randomly perturbed domain the perturbation being small introducing a random mapping these equations are transformed into pdes on a fixed reference domain with random coefficients under suitable assumptions on the random mapping and the input data in particular the so called small data assumption we prove the well posedness of the problem we assume then that the mapping depends affinely on l independent random variables and adopt a perturbation approach expanding the solution with respect to a small parameter e that controls the amount of randomness in the problem we perform an a posteriori error analysis for the first order approximation error namely the error between the exact random solution and the finite element approximation of the first term in the expansion with respect to e numerical results are given to illustrate the theoretical results and the effectiveness of the error estimators

modular vs non modular preconditioners for fluid structure systems with large added mass effect in this article we address the numerical simulation of fluid structure interaction fsi problems featuring large added mass effect we analyze different preconditioners for the coupled system matrix obtained after space time discretization and linearization of the fsi problem the classical dirichlet neumann preconditioner has the advantage of modularity because it allows to reuse existing fluid and structure codes with minimum effort simple interface communication unfortunately its performance is very poor in case of large added mass effects alternatively we consider two non modular approaches the first one consists in preconditioning the coupled system with a suitable diagonal scaling combined with an ilut preconditioner the system is then solved by a krylov method the drawback of this procedure is that the combination of fluid and structure codes to solve the coupled system is not straightforward the second non modular approach we consider is a splitting technique based on an inexact block lu factorization of the linear fsi system the resulting algorithm computes the fluid velocity separately from the coupled pressure structure system at each iteration reducing the computational cost independently of the preconditioner the efficiency of semi implicit algorithms i e those that treat geometric and fluid nonlinearities in an explicit way is highlighted and their performance compared to the one of implicit algorithms all the methods are tested on three dimensional blood vessel systems the algorithm combining the non modular ilut preconditioner with krylov methods proved to be the fastest

weight spectrum of codes associated with the grassmannian g 3 7 in this paper we consider the problem of determining the weight spectrum of q ary codes c 3 m associated with grassmann varieties g 3 m for m 6 this was done in a paper by nogin in 1997 we derive a formula for the weight of a codeword of c 3 m in terms of certain varieties associated with alternating trilinear forms on fqm the classification of such forms under the action of the general linear group gl m fq is the other component that is required to calculate the spectrum of c 3 m for m 7 we explicitly determine the varieties mentioned above the classification problem for alternating three forms on fq7 was solved in a study by cohen and helminck in 1988 which we then use to determine the spectrum of c 3 7

constraint field systems in multimomentum canonical variables to describe constraint field models we apply the multimomentum hamiltonian formalism where momenta correspond to derivatives of fields with respect to all world coordinates not only time if a lagrangian density is degenerate the euler lagrange equations are underdetermined and need additional gauge type conditions which remain elusive in general one gets these conditions automatically as a part of the hamilton equations but must consider a family of hamiltonian forms associated with the same lagrangian density in order to exhaust solutions of the euler lagrange equations the case of degenerate quadratic and affine lagrangian densities is elaborated as a result we get the universal procedure of describing constraint field systems

convergence of a fluid structure interaction problem decoupled by a neumann control over a single time step abstract building off of previous analytical results for recasting fluid structure interaction into an optimal control setting an a priori error estimate is given for the optimality system by means of brr theory the convergence of the steepest descent method is proven in a discrete setting for a sufficiently small time step and mesh size a numerical study is included supporting the theoretical rate of convergence over a single time step additional results demonstrate optimal convergence in space and time over several time steps

on some pressure segregation methods of fractional step type for the finite element approximation of incompressible flow problems abstract in this paper we treat several aspects related to time integration methods for the incompressible navier stokes equations that allow to uncouple the calculation of the velocities and the pressure the first family of schemes consists of classical fractional step methods of which we discuss several possibilities for the pressure extrapolation and the time integration of first and second order the second family consists of schemes based on an explicit treatment of the pressure in the momentum equation followed by a poisson equation for the pressure it turns out that this staggered treatment of the velocity and the pressure is stable finally we present predictor corrector methods based on the above schemes that aim to converge to the solution of the monolithic time integration method apart from presenting these schemes and check its numerical performance we also present a complete set of stability results for the fractional step methods that are independent of the space stability of the velocity pressure interpolation that is of the classical inf sup condition

regularity properties of fiber derivatives associated with higher order mechanical systems the aim of this work is to study fiber derivatives associated to lagrangian and hamiltonian functions describing the dynamics of a higher order autonomous dynamical system more precisely given a function in t t k 1 q we find necessary and sufficient conditions for such a function to describe the dynamics of a kth order autonomous dynamical system thus being a kth order hamiltonian function then we give a suitable definition of hyper regularity for these higher order hamiltonian functions in terms of their fiber derivative in addition we also study an alternative characterization of the dynamics in lagrangian submanifolds in terms of the solutions of the higher order euler lagrange equations

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

nk almost tangent structures and the hamiltonization of higher order field theories in this paper a new interpretation of the hamiltonization of higher order lagrangian field theories is given introducing a new class of tensor fields of type 1 1 that extends almost tangent structures to the tangent bundle of nk velocities

high order finite element methods for moving boundary problems with prescribed boundary evolution abstract we introduce a framework for the design of finite element methods for two dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy both in space and in time at the core of our approach is the use of a universal mesh a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the moving boundary the resulting method maintains an exact representation of the prescribed moving boundary at the discrete level or an approximation of the appropriate order yet is immune to large distortions of the mesh under large deformations of the domain the framework is general making it possible to achieve any desired order of accuracy in space and time by selecting a preferred and suitable finite element space on the universal mesh for the problem at hand and a preferred and suitable time integrator for ordinary differential equations we illustrate our approach by constructing a particular class of methods and apply them to a prescribed boundary variant of the stefan problem we present numerical evidence for the order of accuracy of our schemes in one and two dimensions

analysis of a stabilized finite element approximation of the transient convection diffusion equation using an ale framework in this paper we analyze a stabilized finite element method to approximate the convection diffusion equation on moving domains using an arbitrary lagrangian eulerian ale framework as basic numerical strategy we discretize the equation in time using first and second order backward differencing bdf schemes whereas space is discretized using a stabilized finite element method the orthogonal subgrid scale formulation to deal with convection dominated flows the semidiscrete problem continuous in space is first analyzed in this situation it is easy to identify the error introduced by the ale approach after that the fully discrete method is considered we obtain optimal error estimates in both space and time in a mesh dependent norm the analysis reveals that the ale approach introduces an upper bound for the time step size for the results to hold the results obtained for the fully discretized second order scheme in time are associated to a weaker norm than the one used for the first order method nevertheless optimal convergence results have been proved for fixed domains we recover stability and convergence results with the strong norm for the second order scheme stressing the aspects that make the analysis of this method much more involved

on some time marching schemes for the stabilized finite element approximation of the mixed wave equation abstract in this paper we analyze time marching schemes for the wave equation in mixed form the problem is discretized in space using stabilized finite elements on the one hand stability and convergence analyses of the fully discrete numerical schemes are presented using different time integration schemes and appropriate functional settings on the other hand we use fourier techniques also known as von neumann analysis in order to analyze stability dispersion and dissipation numerical convergence tests are presented for various time integration schemes polynomial interpolations for the spatial discretization stabilization methods and variational forms to analyze the behavior of the different schemes considered a 1d wave propagation problem is solved

interface stabilised finite element method for moving domains and free surface flows abstract a recently developed stabilised finite element method which draws upon features of both continuous and discontinuous finite element methods is generalised for the incompressible navier stokes equations on moving domains and for free surface problems the approach allows the natural incorporation of upwinding of the advective flux and the formulation is stable when using equal order lagrange basis functions for the velocity and pressure fields particular attention is paid to the formulation of a fractional step algorithm for moving domain problems numerous applications to environmental free surface flows are presented ranging from simple test cases to simulations of sophisticated laboratory experiments it is shown that the formulation which contains no flow dependent stabilisation parameters is able to model a wide range of flow conditions stably without user intervention and it is shown that negligible numerical dissipation is introduced the physics of the considered numerical examples involves sensitive free surface wave behaviour which has been accurately captured due to the stability of the model together with negligible introduced numerical dissipation

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

unified analysis of finite element methods for problems with moving boundaries we present a unified analysis of finite element methods for problems with prescribed moving boundaries in particular we study an abstract parabolic problem posed on a moving domain with prescribed evolution discretized in space with a finite element space that is associated with a moving mesh that conforms to the domain at all times the moving mesh is assumed to evolve smoothly in time except perhaps at a finite number of remeshing times where the solution is transferred between finite element spaces via a projection a key result of our analysis is an abstract estimate for the l 2 norm of the error between the exact and semidiscrete solutions at a fixed positive time expressed in terms of the total variation in time of a quantity that measures the difference between the exact solution at time t and its elliptic projection onto the finite element space at time t specializing the abstract estimate to particular choices of the mesh motion strategy finite element space and projector leads to e

fully discrete error estimation for a quasi newtonian fluid structure interaction problem we consider an incompressible quasi newtonian fluid structure interaction fsi problem formulated in a monolithic framework where the matching conditions at the moving interface are satisfied the fully discretized fsi system is discussed with detailed analysis for the stability and error estimate as well as numerical experiments that confirm the theoretical results

duals of affine grassmann codes and their relatives affine grassmann codes are a variant of generalized reed muller codes and are closely related to grassmann codes these codes were introduced in a recent work by beelen here we consider more generally affine grassmann codes of a given level we explicitly determine the dual of an affine grassmann code of any level and compute its minimum distance further we ameliorate the results by beelen concerning the automorphism group of affine grassmann codes finally we prove that affine grassmann codes and their duals have the property that they are linear codes generated by their minimum weight codewords this provides a clean analogue of a corresponding result for generalized reed muller codes

stability and geometric conservation laws for ale formulations the aim of this paper is to investigate a model ale scheme with respect to various possible choices of time discretizations for each time scheme we investigate the relationships between stability and the so called geometric conservation laws gcl we shall see that gcl condition proves neither necessary nor sufficient for stability in doing so we review some known theoretical results and we prove some new stability results for space time ale discretizations some new error estimates are also presented several numerical experiments confirm the theory

higher order conditions for singular lagrangian dynamics for a kth order singular lagrangian the presymplectic equation plus the different mth order differential equation conditions that can be considered in the lagrangian space yield different dynamics which are studied this leads to a new classification of the constraints this study is also performed in the intermediate formalisms which can be defined between the lagrangian and the hamiltonian ones the corresponding classification schemes are then related

an alternative approach to the cartan form in lagrangian field theories an operator analogous to the almost tangent structure on a tangent bundle is defined on jet bundles of a fibred manifold this operator is used to construct a cartan form the construction is unique for first order lagrangians and is also unique when restricted to higher order mechanics

higher order lagrangian systems geometric structures dynamics and constraints in order to study the connections between lagrangian and hamiltonian formalisms constructed from a perhaps singular higher order lagrangian some geometric structures are constructed intermediate spaces between those of lagrangian and hamiltonian formalisms partial ostrogradski s transformations and unambiguous evolution operators connecting these spaces are intrinsically defined and some of their properties studied equations of motion constraints and arbitrary functions of lagrangian and hamiltonian formalisms are thoroughly studied in particular all the lagrangian constraints are obtained from the hamiltonian ones once the gauge transformations are taken into account the true number of degrees of freedom is obtained both in the lagrangian and hamiltonian formalisms and also in all the intermediate formalisms herein defined

unambiguous formalism for higher order lagrangian field theories the aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories and implies the existence of different cartan forms and legendre transformations we propose a differential geometric setting for the dynamics of a higher order field theory based on the skinner and rusk formalism for mechanics this approach incorporates aspects of both the lagrangian and the hamiltonian description since the field equations are formulated using the lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual as both of these objects are uniquely defined the skinner rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions the result is that we obtain a unique and global intrinsic version of the euler lagrange equations for higher order field theories several examples illustrate our construction

stabilization of incompressibility and convection through orthogonal sub scales in finite element methods two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper the first of them is the stabilization through the pressure gradient projection which consists of adding a certain least squares form of the difference between the pressure gradient and its l2 projection onto the discrete velocity space in the variational equations of the problem the second is a sub grid scale method whose stabilization effect is very similar to that of the galerkin least squares gls method for the stokes problem it is shown here that the first method can also be recast in the framework of sub grid scale methods with a particular choice for the space of sub scales this leads to a new stabilization procedure whose applicability to stabilize convection is also studied in this paper

multisymplectic unified formalism for einstein hilbert gravity we present a covariant multisymplectic formulation for the einstein hilbert model of general relativity as it is described by a second order singular lagrangian this is a gauge field theory with constraints the use of the unified lagrangian hamiltonian formalism is particularly interesting when it is applied to these kinds of theories since it simplifies the treatment of them in particular the implementation of the constraint algorithm the retrieval of the lagrangian description and the construction of the covariant hamiltonian formalism in order to apply this algorithm to the covariant field equations they must be written in a suitable geometrical way which consists of using integrable distributions represented by multivector fields of a certain type we apply all these tools to the einstein hilbert model without and with energy matter sources we obtain and explain the geometrical and physical meaning of the lagrangian constraints and we construct the multimomentum covariant hamiltonian formalisms in both cases as a consequence of the gauge freedom and the constraint algorithm we see how this model is equivalent to a first order regular theory without gauge freedom in the case of the presence of energy matter sources we show how some relevant geometrical and physical characteristics of the theory depend on the type of source in all the cases we obtain explicitly multivector fields which are solutions to the gravitational field equations finally a brief study of symmetries and conservation laws is done in this context we present a covariant multisymplectic formulation for the einstein hilbert model of general relativity as it is described by a second order singular lagrangian this is a gauge field theory with constraints the use of the unified lagrangian hamiltonian formalism is particularly interesting when it is applied to these kinds of theories since it simplifies the treatment of them in particular the implementation of the constraint algorithm the retrieval of the lagrangian description and the construction of the covariant hamiltonian formalism in order to apply this algorithm to the covariant field equations they must be written in a suitable geometrical way which consists of using integrable distributions represented by multivector fields of a certain type we apply all these tools to the einstein hilb

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100