metriques de carnot cartheodory et quasiisometries des espaces symetriques de rang un we exhibit a rigidity property of the simple groups sp n 1 and f7 20 which implies mostow rigidity this property does not extend to o n 1 and u n 1 the proof relies on quasiconformal theory applied in the cr setting extensions are given to a class of solvable lie groups as a byproduct a result on quasiisometries of infinite nilpotent groups is obtained dans cet article on etablit une propriete de rigidite des groupes simples de rang un sp n 1 n 2 2 et fqui entraine la rigidite de mostow 1 theoreme toute quasiisornwtrie de 1 espace hyperbolique quaternionien hhn n 2 resp du plan hyperbolique de cayley cah2 est d distance bornee d une isometrie i e differe d une isomnetrie par une application qui diplace les points d une distance bornee une application f entre espaces metriques est une quasiisometrie s il existe des constantes l et c telles que l image de f soit c dense et que pour tous x y c d x y d fx fy ld x y c l une quasiisometrie entre des g et g est une sorte d isomorphisme virtuel dans la categorie topologique en effet cela correspond a une action de g sur un fibre principal c de groupe g sur une base compacte cf ra un isomorphisme entre sous groupes cocompacts covolume fini suffit pour les groupes simples de rang un de groupes de lie s etend en une quasiisometrie des espaces symetriques ou des groupes de lie si celle ci est proche d une isometrie des espaces symetriques resp un isomorphisme des groupes de lie les sous groupes sont conjugues c est la rigidite de mostow m2 la propriete ci dessus ne s etend pas aux groupes o n 1 et u n 1 en effet paragraphe 11 7 ceux ci ont beaucoup de quasiisometries au moins this content downloaded from 207 46 13 92 on sun 20 nov 2016 04 26 46 utc all use subject to http about jstor org terms

finite element solution of compressible viscous flows using conservative variables abstract a finite element method for solving the compressible navier stokes equations is presented these equations are solved in conservation form and using conservative variables appropriate finite element approximations are discussed when a galerkin variational formulation is used for high speed flows the formulation is stabilized using the stream line upwind petrov galerkin method for which we propose an analytical expression for the matrix a new discontinuity capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients the non linear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual gmres algorithm numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed finite element method

global target aggregation and state agreement of nonlinear multi agent systems with switching topologies in this paper we discuss coordination problems of a group of autonomous agents including the target aggregation to a convex set and the state agreement the aggregation of the whole agent group consisting of leaders informed agents and followers to a given set is investigated with switching interconnection topologies described by the connectivity assumptions on the joint topology in the time interval t for any time t and then the state agreement problem is studied in a similar way an approach based on set stability and limit set analysis is given to study the multi agent convergence problems with the help of graph theory and convex analysis coordination conditions are obtained in some important cases and the results show that simple local rules can make the networked agents with first order nonlinear individual dynamics achieve desired collective behaviors

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

a comparative study of different sets of variables for solving compressible and incompressible flows a globally conservative galerkin least squares formulation which attains correct shock structure is developed for any choice of variables only the choice of entropy variables satisfies exactly the discrete clausius duhem inequality without any dissipative mechanisms whereas for the rest of the variables artificial diffusion is required to guarantee entropy production the limit of the formulation is well defined for entropy variables and the primitive variables p u t leading to conservative incompressible formulations the approach is stable for any continuous interpolations both for compressible and incompressible flows a comparative study of different variables is performed indicating that entropy variables and the primitive variables p u t possess the most attributes for practical problem solving

an unstructured finite elements method for solving the compressible rans equations and the spalart allmaras turbulence model this paper deals with a stabilized finite element method for solving the compressible navier stokes equations combined with the spalart allmaras turbulence model the aim is to assess the ability of this formulation to solve high reynolds number turbulent flows over anisotropic meshes this formulation lies in the framework of the stream line upwind petrove galerkin method we propose a simple and efficient formulation for the stabilization matrix and develop a shock capturing operator numerical tests on the 3d boundary layer over a flat plate and on the onera m6 wing show the stability and robustness of the proposed method

supg finite element computation of compressible flows with the entropy and conservation variables formulations abstract supg stabilized finite element formulations of compressible euler equations based on the conservation and entropy variables are investigated and compared the formulation based on the conservation variables consists of the formulation introduced by tezduyar and hughes plus a shock capturing term the formulation based on the entropy variables is the same as the one by hughes franca and mallet which has a shock capturing term built in these formulations are tested on several subsonic transonic and supersonic compressible flow problems it is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables furthermore the solutions obtained using the two formulations are very close and in some cases almost indistinguishable consequently it can be deduced that the relative merits of these two formulations will continue to remain under debate

simple stabilizing matrices for the computation of compressible flows in primitive variables the key ingredient that balances stability and accuracy in stabilized formulations is the parameter of intrinsic time scales for multi dimensional hyperbolic systems of equations this parameter is a matrix and the available expressions for its computation involve the solution of an eigenvalue problem which can be tedious or cpu time consuming thus for formulations based on primitive variables including pressure a couple of simple stabilizing matrices are presented which are easy to implement and cpu economic numerical evaluations show the performance of the various choices

coarse differentiation of quasi isometries ii rigidity for sol and lamplighter groups in this paper we prove quasi isometric rigidity results concerning lattices in sol and lamplighter groups the paper builds in a substantial way on our earlier paper coarse dierentiation of quasi isometries i spaces not quasi isometric to cayley graphs

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 shock hydrodynamics ii design and physical interpretation of the supg operator for lagrangian computations abstract a new supg stabilized formulation for lagrangian hydrodynamics of materials satisfying the mie gruneisen equation of state was presented in the first paper of the series g scovazzi m a christon t j r hughes j n shadid stabilized shock hydrodynamics i a lagrangian method comput methods appl mech engrg in press doi 10 1016 j cma 2006 08 008 the present article investigates in more detail the design of the supg stabilization operator focusing on its multiscale and physical interpretations connections with the analysis of kuropatenko v f kuropatenko on difference methods for the equations of hydrodynamics in n n janenko ed difference methods for solutions of problems of mathematical physics i american mathematical society providence ri 1967 for discontinuity capturing operators in the limit of weak shocks are shown galilean invariance requirements for the supg operator are explored and corroborated by numerical evidence this work is intended to elucidate the profound physical significance of the supg operator as a subgrid interaction model

algebraic approximation of sub grid scales for the variational multiscale modeling of transport problems abstract variational multiscale vms finite element methods fems are robust for the development of general formulations for the solution of multiphysics and multiscale transport problems to obtain a tractable and computationally efficient model vms methods often rely on a residual based algebraic approximation of the sub grid scales small or unresolved features of the solution field not captured by the discretization using a so called intrinsic time scales matrix which depends on the problem s overall differential operator and represents the main model parameter a novel technique for approximating the intrinsic time scales matrix for generic transport problems in a relatively inexpensive manner e g does not rely on eigenvalue computations is presented the method is denoted transport equivalent scaling tes and is based on the monolithic casting of the transport problem as a system of transient advective diffusive reactive tadr equations and a subsequent scaling of the coefficient matrices such to preserve each type of transport flux an algebraic vms formulation incorporating the tes method is complemented with a discontinuity capturing dc approach and implemented within a fem solver for the solution of tadr problems the solution of the global discrete system is accomplished using a generalized alpha time stepper together with a globalized inexact newton krylov nonlinear solver the effectiveness of the tes formulation is verified with the simulation of benchmark incompressible compressible and magnetohydrodynamic flow problems the results demonstrate that the tes method seamlessly handles incompressible compressible flows in a unified manner e g without assessing the compressibility of the flow the convergence process using the tes approach and a more standard approximation for the intrinsic time scales as well as the effect of the dc approach are also investigated analysis of the intrinsic time scales for a one dimensional incompressible flow model reveals the similitudes and differences between the tes formulation and other conventional methods

stabilized residual distribution for shallow water simulations we propose a stabilized residual distribution rd scheme for the simulation of shallow water flows the final discretization is obtained combining the stabilized rd approach proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 with the conservative formulation already used in ricchiuto et al j comp phys 222 2007 to simulate shallow water flows the scheme proposed is a nonlinear variant of a lax friedrichs type discretization it is well balanced it actually yields second order of accuracy in smooth areas and it preserves the positivity of the height of the water in presence of dry areas this is made possible by the residual character of the discretization by properly adapting the stabilization operators proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 and thanks to the positivity preserving character of the underlying lax friedrichs scheme we demonstrate the properties of the discretization proposed on a wide variety of tests

on distributed convex optimization under inequality and equality constraints we consider a general multi agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint a global equality constraint and a global constraint set the objective function is defined by a sum of local objective functions while the global constraint set is produced by the intersection of local constraint sets in particular we study two cases one where the equality constraint is absent and the other where the local constraint sets are identical we devise two distributed primal dual subgradient algorithms based on the characterization of the primal dual optimal solutions as the saddle points of the lagrangian and penalty functions these algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the slater s condition

on metric ramsey type phenomena the main question studied in this article may be viewed as a nonlinear analogue of dvoretzky s theorem in banach space theory or as part of ramsey theory in combinatorics given a finite metric space on n points we seek its subspace of largest cardinality which can be embedded with a given distortion in hilbert space we provide nearly tight upper and lower bounds on the cardinality of this subspace in terms of n and the desired distortion our main theorem states that for any 0 every n point metric space contains a subset of size at least n1 which is embeddable in hilbert space with o log 1 distortion the bound on the distortion is tight up to the log 1 factor we further include a comprehensive study of various other aspects of this problem

a better consistency for low order stabilized finite element methods abstract the standard implementation of stabilized finite element methods with a piece wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy the popularity of these low order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space this new method is seen to engender a stronger consistency leading to better convergence and improved accuracy applications to the navier stokes equations are given which illustrate the improvement at a negligible additional cost

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

distributed constrained optimal consensus of multi agent systems we study a distributed optimal consensus problem of continuous time multi agent systems with a common state set constraint each agent is assigned with an individual cost function which is coercive and convex a distributed control protocol is to be designed to guarantee a consensus and in the meanwhile reach the minimizer of the aggregate cost functions within the constraint set three terms are included in the protocol local averaging local projection and local subgradient with a diminishing but persistent gain it is shown that the constrained optimal consensus can be achieved under a uniformly jointly connected communication network with bounded time varying edge weights

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

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

a discourse on galilean invariance supg stabilization and the variational multiscale framework abstract galilean invariance is one of the key requirements of many physical models adopted in theoretical and computational mechanics spurred by recent research developments in shock hydrodynamics computations g scovazzi stabilized shock hydrodynamics ii design and physical interpretation of the supg operator for lagrangian computations comput methods appl mech engrg in press doi 10 1016 j cma 2006 08 009 a detailed analysis on the principle of galilean invariance in the context of supg operators is presented it was observed in g scovazzi in press that lack of galilean invariance can yield catastrophic instabilities in lagrangian computations here the analysis develops at a more general level and an arbitrary lagrangian eulerian ale formulation is used to explain how to consistently derive galilean invariant supg operators stabilization operators for lagrangian and eulerian mesh computations are obtained as limits of the stabilization operator for the underlying ale formulation in the case of eulerian meshes it is shown that most of the supg operators designed for compressible flow computations to date are not consistent with galilean invariance it is stressed that galilean invariant supg formulations can provide consistent advantages in the context of complex engineering applications due to the simple modifications needed for their implementation

stabilized shock hydrodynamics i a lagrangian method abstract a new supg stabilized formulation for lagrangian hydrodynamics of materials satisfying mie gruneisen equation of state is proposed it allows the use of simplex type triangular tetrahedral meshes as well as the more commonly used brick type quadrilateral hexahedral meshes the proposed method yields a globally conservative formulation in which equal order interpolation p1 or q1 isoparametric finite elements is applied to velocities displacements and pressure as a direct consequence and in contrast to traditional cell centered multidimensional hydrocode implementations the proposed formulation allows a natural representation of the pressure gradient on element interiors the supg stabilization involves additional design requirements specific to the lagrangian formulation a discontinuity capturing operator in the form of a noh type viscosity with artificial heat flux is used to preserve stability and smoothness of the solution in shock regions a set of challenging shock hydrodynamics benchmark tests for the euler equations of gas dynamics in one and two space dimensions is presented in the two dimensional case computations performed on quadrilateral and triangular grids are analyzed and compared these results indicate that the new formulation is a promising technology for hydrocode applications

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

quasi isometric classification of graph manifold groups we show that the fundamental groups of any two closed irreducible nongeometric graph manifolds are quasi isometric we also classify the quasi isometry types of fundamental groups of graph manifolds with boundary in terms of certain finite twocolored graphs a corollary is the quasi isometric classification of artin groups whose presentation graphs are trees in particular any two right angled artin groups whose presentation graphs are trees of diameter greater than 2 are quasi isometric further this quasi isometry class does not include any other right angled artin groups a finitely generated group can be considered geometrically when endowed with a word metric up to quasi isometric equivalence such metrics are unique in this article only finitely generated groups are considered given a collection of groups g gromov 11 proposed the fundamental questions of identifying which groups are quasi isometric to those in g rigidity and which groups in g are quasi isometric to each other classification in this article we focus on the classification question for graph manifold groups and right angled artin groups a compact 3 manifold m is called geometric if m m admits a geometric structure in the sense of thurston i e a complete locally homogeneous riemannian metric of finite volume thurston s geometrization conjecture see 29 17 21 23 22 provides that every irreducible 3 manifold of zero euler characteristic i e with boundary consisting only of tori and klein bottles admits a decomposition along tori and klein bottles into geometric pieces the minimal such decomposition being called the geometric decomposition there is a considerable literature on quasi isometric rigidity and classification of 3 manifold groups the rigidity results can be briefly summarized in the following form

on the quantitative quasi isometry problem transport of poincare inequalities and different types of quasi isometric distortion growth abstract we consider a quantitative form of the quasi isometry problem we discuss several arguments which lead us to a number of results and bounds of quasi isometric distortion comparison of volumes connectivity etc then we study the transport of poincare constants by quasi isometries and we give sharp lower and upper bounds for the homotopy distortion growth for a certain class of hyperbolic metric spaces a quotient of a heintze group r r n by z n we also prove the linear distortion growth between hyperbolic space h n n 3 and a tree

a simple stabilized finite element method for solving two phase compressible incompressible interface flows abstract when computing interface flows between compressible gas and incompressible liquid fluids one faces at least to the following difficulties 1 transition from a gas density linked to the local temperature and pressure by an equation of state to a liquid density mainly constant in space 2 proper approximation of the divergence constraint in incompressible regions and 3 wave transmission at the interface the aim of the present paper is to design a global i e the same for each phase numerical method to address easily this coupling to this end the same set of primitive unknowns and equations is used everywhere in the flow but with a dynamic parameterization that changes from compressible to incompressible regions on one hand the compressible navier stokes equations are considered under weakly compressibility assumption so that a non conservative formulation can be used on the other hand the incompressible non isothermal model is retained in addition the level set transport equation is used to capture the interface position needed to identify the local characteristics of the fluid and to recover the adequate local modelling for space approximation of navier stokes equations a galerkin least squares finite element method is used two essential elements for defining this numerical scheme are the stabilization and the computation of element integral of the approximated weak form since very different concerns motivate the need for stabilization in compressible and incompressible flows the first difficulty is to design a stabilization operator suitable for both types of flows especially in mixed elements in addition some integral of discontinuous functions must be correctly computed to ensure interfacial wave transmission to overcome these two difficulties specific averages are computed especially near the interface finally the level set transport equation is computed by a quadrature free discontinuous galerkin method numerical strategies are performed and validated for 1d and 2d applications

orlicz spaces and the large scale geometry of heintze groups we consider an orlicz space based cohomology for metric measured spaces with bounded geometry we prove the quasi isometry invariance for a general young function in the hyperbolic case we prove that the degree one cohomology can be identified with an orlicz besov function space on the boundary at infinity we give some applications to the large scale geometry of homogeneous spaces with negative curvature heintze groups as our main result we prove that if the heintze group is not of carnot type any self quasi isometry fixes a distinguished point on the boundary and preserves a certain foliation on the complement of that point

a velocity stress mixed stabilized nodal finite element for elastodynamics analysis and computations with strongly and weakly enforced boundary conditions abstract a new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain our method is based on equal order interpolation discrete spaces for both the velocity or displacement and stress or strain tensor variables the mixed form is derived using either the velocity stress or velocity strain pair of unknowns the latter being instrumental in extensions of the method to nonlinear mechanics the proposed approach works equally well on hexahedral or tetrahedral grids and for this reason it is suitable for time domain engineering applications in complex geometry the peculiarity of the proposed approach is the use of the rate form of the stress update equation which yields a set of governing equations with the structure of a non dissipative space time friedrichs system we complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity or displacement weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes because they do not require dedicated data structures for the imposition of the boundary degrees of freedom but rather they utilize the structure of the variational formulation we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi domain simulations of heterogeneous media a complete analysis including stability and convergence proofs is included in the case of a space time variational approach a series of computational tests are used to demonstrate and verify the performance of the proposed approach

local preconditioning and variational multiscale stabilization for euler compressible steady flow abstract this paper introduces a preconditioned variational multiscale stabilization p vms method for compressible flows in this introductory paper we focus on inviscid flow and steady state problems the euler equations are solved on fully unstructured grids and discretized using the finite element method the p vms method can be decomposed into three parts first a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of mach numbers then the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations in this paper the solution is advanced in time using a fully explicit time discretization although p vms is general and can be applied to fully implicit solvers the proposed method is assessed by comparing convergence and accuracy of the solutions between the non preconditioned and preconditioned cases in particular for van leer lee roe s 1991 and choi merkle s 1993 preconditioners in some selected examples covering a large range of mach numbers

coarse differentiation of quasi isometries i spaces not quasi isometric to cayley graphs in this paper we prove that certain spaces are not quasi isometric to cayley graphs of nitely generated groups in particular we answer a question of woess and prove a conjecture of diestel and leader by showing that certain homogeneous graphs are not quasi isometric to a cayley graph of a nitely generated group this paper is the rst in a sequence of papers proving results announced in our 2007 article quasi isometries and rigidity of solvable groups in particular this paper contains many steps in the proofs of quasi isometric rigidity of lattices in sol and of the quasi isometry classication of lamplighter groups the proofs of those results are completed in coarse dierentiation of quasi isometries ii rigidity for lattices in sol and lamplighter groups the method used here is based on the idea of coarse dierentiation introduced in our 2007 article

quasisymmetric maps on the boundary of a negatively curved solvable lie group we describe all the self quasisymmetric maps on the ideal boundary of a particular negatively curved solvable lie group as applications we derive some rigidity properties for quasiisometries of the solvable lie group

quasi isometries preserve the geometric decomposition of haken manifolds we prove quasi isometry invariance of the canonical decomposition for fundamental groups of haken 3 manifolds with zero euler characteristic we show that groups quasi isometric to haken manifold groups with nontrivial canonical decomposition are finite extensions of haken orbifold groups as a by product we describe all 2 dimensional quasi flats in the universal covers of non geometric haken manifolds

a unified approach to compressible and incompressible flows abstract we present a finite element formulation for solving the compressible navier stokes equations which accommodates the use of any set of variables if primitive variables p u t or entropy variables are used the incompressible limit is well behaved therefore one formulation can be used to solve both compressible and incompressible flows

reaching an optimal consensus dynamical systems that compute intersections of convex sets in this paper multi agent systems minimizing a sum of objective functions where each component is only known to a particular node is considered for continuous time dynamics with time varying interconnection topologies assuming that each node can observe a convex solution set of its optimization component and the intersection of all such sets is nonempty the considered optimization problem is converted to an intersection computation problem by a simple distributed control rule the considered multi agent system with continuous time dynamics achieves not only a consensus but also an optimal agreement within the optimal solution set of the overall optimization objective directed and bidirectional communications are studied respectively and connectivity conditions are given to ensure a global optimal consensus in this way the corresponding intersection computation problem is solved by the proposed decentralized continuous time algorithm we establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non smooth analysis

computation of compressible and incompressible flows with a space time stabilized finite element method abstract this paper presents the numerical results of compressible and incompressible flow problems through a unified approach based on a stabilized space time finite element method the numerical approach is continuous in space and discontinuous in time the proposed method starts by the use of a stabilized space time variational formulation which allows the use of the same order interpolation functions for all solution variables the numerical technique is tested through comparison with standard compressible and incompressible flow benchmarks compressible flow cases include 1d and 2d shock problems incompressible flow cases include lid driven cavity flow and flow over a backward facing step computed over a range of r e numbers the results demonstrate high stability and accuracy of the numerical technique over a wide range of flow regimes suggesting straightforward extension to many flow cases not yet investigated

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