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

on inf sup stabilized finite element methods for transient problems we consider the behavior of inf sup stabilization in the context of transient problems with multiple time scales our motivation for studying this setting is provided by reacting flows problems for which small time steps are necessary in the integration process we show that for algorithms defined through a process wherein spatial and temporal discretizations are separated the coupling of implicit time integration with spatial inf sup stabilization may lead to anomalous pressure behavior including the onset of spurious oscillations for very small time steps effectively this coupling introduces a stability criterion resulting in a dependence between the spatial grid size and the time step we illustrate our theoretical results by numerical examples that demonstrate the stability criterion 2004 elsevier b v all rights reserved

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

stabilized finite element methods for the velocity pressure stress formulation of incompressible flows abstract formulated in terms of velocity pressure and the extra stress tensor the incompressible navier stokes equations are discretized by stabilized finite element methods the stabilized methods proposed are analyzed for a linear model and extended to the navier stokes equations the numerical tests performed confirm the good stability characteristics of the methods these methods are applicable to various combinations of interpolation functions including the simplest equal order linear and bilinear elements

a taxonomy of consistently stabilized finite element methods for the stokes problem stabilized mixed methods can circumvent the restrictive inf sup condition without introducing penalty errors for properly chosen stabilization parameters these methods are well posed for all conforming velocity pressure pairs however their variational forms have widely varying properties first stabilization offers a choice between weakly or strongly coercive bilinear forms that give rise to linear systems with identical solutions but very different matrix properties second coercivity may be conditional upon a proper choice of a stabilizing parameter here we focus on how these two aspects of stabilized methods affect their accuracy and efficient iterative solution we present results that indicate a preference of krylov subspace solvers for strongly coercive formulations stability criteria obtained by finite element and algebraic analyses are compared with numerical experiments while for two popular classes of stabilized methods sufficient stability bounds correlate well with numerical stability our experiments indicate the intriguing possibility that the pressure stabilized galerkin method is unconditionally stable

convergence in norm of modified krasnoselski mann iterations for fixed points of demicontractive mappings abstract this paper deals with fixed points methods related to the general class of demicontractive mappings including the well known classes of nonexpansive and quasi nonexpansive mappings in hilbert spaces specifically we point out some historical aspects concerning the concept of demicontactivity and we investigate a regularized variant of the krasnoselski mann iteration that can be alternatively regarded as a simplified form of the inertial iteration p e mainge j math anal appl 344 2008 876 887 with non constant relaxation factors these two methods ensure the strong convergence of the generated sequence towards the least norm element of the set of fixed points of demicontractive mappings however for convergence our method does not require anymore the knowledge of some constant related to the involved demicontractive operator a new and simpler proof is also proposed for its convergence even when involving non constant relaxation factors we point out the simplicity of this algorithm at least from computational point of view in comparison with other existing methods we also present some numerical experiments concerning a convex feasibility problem experiments that emphasize the characteristics of the considered algorithm comparing with a classical cyclic projection type iteration

improving stability of stabilized and multiscale formulations in flow simulations at small time steps abstract the objective of this paper is to show that use of the element vector based definition of stabilization parameters introduced in t e tezduyar computation of moving boundaries and interfaces and stabilization parameters int j numer methods fluids 43 2003 555 575 t e tezduyar y osawa finite element stabilization parameters computed from element matrices and vectors comput methods appl mech engrg 190 2000 411 430 circumvents the well known instability associated with conventional stabilized formulations at small time steps we describe formulations for linear advection diffusion and incompressible navier stokes equations and test them on three benchmark problems advection of an l shaped discontinuity laminar flow in a square domain at low reynolds number and turbulent channel flow at friction velocity reynolds number of 395

stability of semidiscrete formulations for parabolic problems at small time steps solutions of direct time integration schemes that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations along with attendant overshoot in time this degradation is not an artifact of the time marching scheme but rather a property of the solution of the semidiscrete formulation itself a critical time step for the onset of spatial oscillations is derived by analogy to singularly perturbed elliptic problems we then propose a simple procedure of spatial stabilization to remove this pathology from implicit time integration schemes without affecting unconditional temporal stability spatially stabilized implicit time integration is free of spurious spatial oscillations at small time steps and numerical experience points to improved temporal accuracy as well

high order discretization of a stable time domain integral equation for 3d acoustic scattering abstract we develop a high order explicit method for acoustic scattering in three space dimensions based on a combined field time domain integral equation the spatial discretization of nystrom type uses gaussian quadrature on panels combined with a special treatment of the weakly singular kernels arising in near neighbor interactions in time a new class of convolution splines is used in a predictor corrector algorithm experiments on a torus and a perturbed torus are used to explore the stability and accuracy of the proposed scheme this involved around one thousand solver runs at up to 8th order and up to around 20 000 spatial unknowns demonstrating 5 9 digits of accuracy in addition we show that parameters in the combined field formulation chosen on the basis of analysis for the sphere and other convex scatterers work well in these cases

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

finite element stabilization parameters computed from element matrices and vectors abstract we propose new ways of computing the stabilization parameters used in the stabilized finite element methods such as the streamline upwind petrov galerkin supg and pressure stabilizing petrov galerkin pspg formulations the parameters are computed based on the element level matrices and vectors which automatically take into account the local length scales advection field and the reynolds number we describe how we compute these parameters in the context of first a time dependent advection diffusion equation and then the navier stokes equations of unsteady incompressible flows

galerkin gradient least squares formulations for transient conduction heat transfer this paper presents the benefits provided by the use of the galerkin gradient least squares ggls method for transient conduction heat transfer the consistency of the gls method for this type of problem is also discussed the ggls method is compared with standard galerkin formulation on problems having an analytical solution a semi infinite solid solved on one and three dimensional meshes and a three dimensional thin plate for three dimensional applications the principle of including gradient least squares terms is extended to stabilize robin convection boundary conditions numerical simulations show that additional boundary gradient least squares terms improve the behavior of the solution on boundaries subject to convection boundary conditions new procedures used to obtain the gls and ggls stabilized finite element formulations are also presented the methodology consists in modifying the equation to be solved and then to obtain the variational equation by a standard galerkin method

a hybrid extragradient viscosity method for monotone operators and fixed point problems this paper deals with an iterative method in a real hilbert space for approximating a common element of the set of fixed points of a demicontractive operator possibly quasi nonexpansive or strictly pseudocontractive and the set of solutions of a variational inequality problem for a monotone lipschitz continuous mapping the considered algorithm can be regarded as a combination of a variation of the hybrid steepest descent method and the so called extragradient method under classical conditions we prove the strong convergence of the sequences of iterates given by the considered scheme

partial representations and partial group algebras abstract the partial group algebra of a group g over a field k denoted by k par g is the algebra whose representations correspond to the partial representations of g over k vector spaces in this paper we study the structure of the partial group algebra k par g where g is a finite group in particular given two finite abelian groups g 1 and g 2 we prove that if the characteristic of k does not divide the order of g 1 then k par g 1 is isomorphic to k par g 2 if and only if g 1 is isomorphic to g 2

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

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

analysis of the pspg method for the transient stokes problem abstract we propose a new analysis for the pspg method applied to the transient stokes problem stability and convergence are obtained under different conditions on the discretization parameters depending on the approximation used in space for the pressure we prove optimal stability and convergence only in the case of piecewise affine approximation under the standard condition on the time step finally we show that the stability problems of the pspg method can be circumvented using an appropriate discrete reconstruction of the laplace operator

iterative methods for the computation of fixed points of demicontractive mappings this paper surveys some of the main convergence properties of the mann type iteration for the demicontractive mappings some variants of the mann iteration that ensure the strong convergence like the cq algorithm and a variant for the asymptotically demicontractive mappings are also considered the usual framework of our study is a real hilbert space and only to a certain extent some particular banach spaces historical aspects are pointed out and some applications for the convex feasibility problem are discussed

projected subgradient techniques and viscosity methods for optimization with variational inequality constraints in this paper we propose an easily implementable algorithm in hilbert spaces for solving some classical monotone variational inequality problem over the set of solutions of mixed variational inequalities the proposed method combines two strategies projected subgradient techniques and viscosity type approximations the involved stepsizes are controlled and a strong convergence theorem is established under very classical assumptions our algorithm can be applied for instance to some mathematical programs with complementarity constraints

associativity of crossed products by partial actions enveloping actions and partial representations given a partial action a of a group g on an associative algebra a we consider the crossed product a g using the algebras of multipliers we generalize a result of exel 1997 on the associativity of a g obtained in the context of c algebras in particular we prove that a g is associative provided that a is semiprime we also give a criterion for the existence of a global extension of a given partial action on an algebra and use crossed products to study relations between partial actions of groups on algebras and partial representations as an application we endow partial group algebras with a crossed product structure

analysis of the small viscosity and large reaction coefficient in the computation of the generalized stokes problem by a novel stabilized finite element method abstract in this paper we propose and analyze a novel stabilized finite element method fem for the system of generalized stokes equations arising from the time discretization of transient stokes problem the system involves a small viscosity which is proportional to the inverse of large reynolds number and a large reaction coefficient which is the inverse of small time step the proposed stabilized fem employs the c 0 piecewise linear elements for both velocity field and pressure on the same mesh and uses the residuals of the momentum equation and the divergence free equation to define the stabilization terms the stabilization parameters are fixed and element independent without a comparison of the viscosity the reaction coefficient and the mesh size using the finite element solution of an auxiliary boundary value problem as the interpolating function for velocity and the h 1 seminorm projection for pressure instead of the usual nodal interpolants we derive error estimates for the stabilized finite element approximations to velocity and pressure in the l 2 and h 1 norms and most importantly we explicitly establish the dependence of error bounds on the viscosity the reaction coefficient and the mesh size our analysis reveals that this stabilized fem is particularly suitable for the generalized stokes system with a small viscosity and a large reaction coefficient which has never been achieved before in the error analysis of other stabilization methods in the literature we then numerically confirm the effectiveness of the proposed stabilized fem comparisons made with other existing stabilization methods show that the newly proposed method can attain better accuracy and stability

circle actions on c algebras partial automorphisms and a generalized pimsner voiculescu exact sequence abstract we introduce a method to study c algebras possessing an action of the circle group from the point of view of their internal structure and their k theory under relatively mild conditions our structure theorem shows that any c algebra where an action of the circle is given arises as the result of a construction that generalizes crossed products by the group of integers such a generalized crossed product construction is carried out for any partial automorphism of a c algebra where by a partial automorphism we mean an isomorphism between two ideals of the given algebra our second main result is an extension to crossed products by partial automorphisms of the celebrated pimsner voiculescu exact sequence for k groups the representation theory of the algebra arising from our construction is shown to parallel the representation theory for c dynamical systems in particular we generalize several of the main results relating to regular and covariant representations of crossed products

on an improved unusual stabilized finite element method for theadvective reactive diffusive equation an improved unusual finite element method is studied herein for a second order linear scalar differential equation including a zero order term the method consists in subtracting from the standard galerkin method a mesh dependent term suggested by static condensation of the bubbles based on this idea a new stabilized parameter is constructed which improves accuracy of the solution several numerical tests attest the efficiency of the present method and an error analysis is perfomed

galois theory for comatrix corings descent theory morita theory frobenius and separability properties el kaoutit and gomez torrecillas introduced comatrix corings generalizing sweedler s canonical coring and proved a new version of the faith fully flat descent theorem they also introduced galois corings as corings isomorphic to a comatrix coring in this paper we further investigate this theory we prove a new version of the joyal tierney descent theorem and generalize the galois coring structure theorem we associate a morita con text to a coring with a fixed comodule and relate it to galois type properties of the coring an affineness criterion is proved in the situation where the cor ing is coseparable further properties of the morita context are studied in the situation where the coring is co frobenius

stabilized finite element method for the transient navier stokes equations based on a pressure gradient projection abstract in this paper we present a stabilized finite element formulation for the transient incompressible navier stokes equations the main idea is to introduce as a new unknown of the problem the projection of the pressure gradient onto the velocity space and to add to the incompresibility equation the difference between the laplacian of the pressure and the divergence of this new vector field this leads to a pressure stabilization effect that allows the use of equal interpolation for both velocities and pressures in the case of the transient equations we consider the possibility of treating the pressure gradient projection either implicitly or explicity in the first case the number of unknowns of the problem is substantially increased with respect to the standard galerkin formulation nevertheless iterative techniques may be used in order to uncouple the calculation of the pressure gradient projection from the rest of unknowns velocity and pressure when this vector field is treated explicitly the increment of computational cost of the stabilized formulation with respect to the galerkin method is very low we provide a stability estimate for the case of the simple backward euler time integration scheme for both the implicit and the explicit treatment of the pressure gradient projection

partial representations of hopf algebras in this work the notion of a partial representation of a hopf algebra is introduced and its relationship with partial actions of hopf algebras is explored given a hopf algebra h one can associate to it a hopf algebroid hpar which has the universal property that each partial representation of h can be factorized by an algebra morphism from hpar we define also the category of partial modules over a hopf algebra h which is the category of modules over its associated hopf algebroid hpar the hopf algebroid structure of hpar enables us to enhance the category of partial h modules with a monoidal structure and such that the algebra objects in this category are the symmetric partial actions some examples of categories of partial h modules are explored in particular we can describe fully the category of partially z2 graded modules