optimal bounds for a lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions optimal bounds for a lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions

convergence of sph method for scalar nonlinear conservation laws this paper is devoted to the study of the convergence of weighted particle approximation of nonlinear multidimensional conservation laws for euler equations the method is closely related to the smooth particle hydrodynamics sph method extension of the original algorithm is proposed we use approximate riemann solvers instead of artificial viscosity in order to stabilize the scheme the mathematical analysis is performed by connecting this new approach with the finite volume scheme convergence of the approximate solution in l loc p p infty towards the unique weak entropy solution of the cauchy problem is obtained in the scalar nonlinear case by using uniqueness of measure valued solutions

the goldie theorem for h semiprime algebras abstract the main result states that under certain assumptions about a hopf algebra h every h semiprime right noetherian h module algebra has a quasi frobenius classical right quotient ring another question treated in the paper is concerned with the extension of h module structures to quotient rings these results have an application to the semiprimeness problem for smash product algebras a h

stabilized finite element methods with shock capturing for advection diffusion problems abstract stabilized fem of streamline diffusion type for advection diffusion problems may exhibit local oscillations in crosswind direction s as a remedy a shock capturing variant of such stabilized schemes is considered as an additional consistent but nonlinear stabilization we prove existence of discrete solutions then we present some a priori and a posteriori estimates finally we address the efficient solution of the arising nonlinear discrete problems

on monotonicity preserving stabilized finite element approximations of transport problems the aim of this work is to design monotonicity preserving stabilized finite element techniques for transport problems as a blend of linear and nonlinear shock capturing stabilization as linear stabilization we consider and analyze a novel symmetric projection stabilization technique based on a local scott zhang projector next we design a weighting of the aforementioned linear stabilization such that when combined with a finite element discretization enjoying a discrete maximum principle usually attained via nonlinear stabilization it does not spoil these monotonicity properties then we propose novel nonlinear stabilization schemes in the form of an artificial viscosity method where the amount of viscosity is proportional to gradient jumps at either finite element boundaries or nodes for the nodal scheme we prove a discrete maximum principle for time dependent multidimensional transport problems numerical experiments support the numerical analysis and we show that the resulting methods prov

on the convergence of a finite element method for a nonlinear hyperbolic conservation law we consider a space time finite element discretization of a time dependent nonlinear hyperbolic conservation law in one space dimension burgers equation the finite element method is higher order accurate and is a petrov galerkin method based on the so called streamline diffusion modification of the test functions giving added stability we first prove that if a sequence of finite element solutions converges boundedly almost everywhere as the mesh size tends to zero to a function u then u is an entropy solution of the conservation law this result may be extended to systems of conservation laws with convex entropy in several dimensions we then prove using a compensated compactness result of murat tartar that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of burgers equation we also consider a further modification of the test functions giving a method with improved shock capturing finally we present the results of some numerical experiments

sum power iterative water filling for multi antenna gaussian broadcast channels in this correspondence we consider the problem of maximizing sum rate of a multiple antenna gaussian broadcast channel bc it was recently found that dirty paper coding is capacity achieving for this channel in order to achieve capacity the optimal transmission policy i e the optimal transmit covariance structure given the channel conditions and power constraint must be found however obtaining the optimal transmission policy when employing dirty paper coding is a computationally complex nonconvex problem we use duality to transform this problem into a well structured convex multiple access channel mac problem we exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the mac which can easily be mapped to the optimal bc policies

dipper donkin algebra as global symmetry of quantum chains we analyse the role of gl2 a quantum group constructed by dipper and donkin 1991 proc london math soc 63 165 211 as a global symmetry for quantum chains and show how to construct all possible hamiltonians for four state quantum chains with gl2 global symmetry in doing this we search for and present all inner actions of gl2 on the clifford algebra c 1 3 we also introduce the corresponding operator algebras invariants and hamiltonians explicitly

skew group algebras of deformed preprojective algebras abstract suppose that q is a finite quiver and g aut q is a finite group k is an algebraic closed field whose characteristic does not divide the order of g for any algebra k q i where i is an arbitrary ideal of path algebra kq we give all the indecomposable g modules from indecomposable modules when g is abelian in particular we apply this result to the deformed preprojective algebra q and get a reflection functor for the module category of q g furthermore we construct a new quiver q g and prove that q g is morita equivalent to q g for some

when is a smash product semiprime a partial answer abstract it is an open question whether the smash product of a semisimple hopf algebra and a semiprime module algebra is semiprime in this paper we show that the smash product of a commutative semiprime module algebra over a semisimple cosemisimple hopf algebra is semiprime in particular we show that the central h invariant elements of the martindale ring of quotients of a module algebra form a von neumann regular and self injective ring whenever a is semiprime for a semiprime goldie pi h module algebra a with central invariants we show that a h is semiprime if and only if the h action can be extended to the classical ring of quotients of a if and only if every non trivial h stable ideal of a contains a non zero h invariant element in the last section we show that the class of strongly semisimple hopf algebras is closed under taking drinfeld twists applying some recent results of etingof and gelaki we conclude that every semisimple cosemisimple triangular hopf algebra over a field is strongly semisimple

an analysis of some high accuracy finite element methods for hyperbolic problems some high accuracy finite element methods for hyperbolic problems are studied in this paper it is proven that over a finite element mesh the convergence order of linear finite element solutions for both linear and nonlinear equations can be higher than one even if the exact solutions are discontinuous the theoretical tools for the convergence analysis are some superclose error estimates that are also developed in this paper for nonsmooth solutions

gorenstein subrings of invariants under hopf algebra actions abstract this paper concerns conditions on the action of a finite dimensional semisimple hopf algebra on an artin schelter regular algebra that force the subring of invariants to satisfy the artin schelter gorenstein condition classical results such as watanabe s theorem and stanley s theorem are extended from the case of a group action to the context of a hopf algebra action a hopf algebra version of the homological determinant is introduced and it becomes an important tool in the generalization from group actions to hopf algebra actions

convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions convergence of a shock capturing streamline diffusion nite element method for a conservation law in two space dimensions

representations of skew group algebras induced from isomorphically invariant modules over path algebras abstract suppose that q is a connected quiver without oriented cycles and is an automorphism of q let k be an algebraically closed field whose characteristic does not divide the order of the cyclic group the aim of this paper is to investigate the relationship between indecomposable kq modules and indecomposable k q k modules it has been shown by hubery that any k q k module is an isomorphically invariant kq module i e ii module in this paper we call it equivalent kq module and conversely any equivalent kq module induces a k q k module in this paper the authors prove that a k q k module is indecomposable if and only if it is an indecomposable equivalent kq module namely a method is given in order to induce all indecomposable k q k modules from all indecomposable equivalent kq modules the number of non isomorphic indecomposable k q k modules induced from the same indecomposable equivalent kq module is given in particular the authors give the relationship between indecomposable k q k modules and indecomposable kq modules in the cases of indecomposable simple projective and injective modules

rota baxter paired modules and their constructions from hopf algebras abstract in this paper we introduce the concept of a rota baxter paired module to study rota baxter modules without necessarily a rota baxter operator we obtain two characterizations of rota baxter paired modules and give some basic properties of rota baxter paired modules beginning with the connection between the notion of integrals in the representations of hopf algebra and of the notion of an integral algebra as a motivation and special case of rota baxter algebra of weight zero we obtain a large number of rota baxter paired modules from hopf related algebras and modules including semisimple hopf algebras weak hopf algebras long bialgebras quasitriangular hopf algebras weak hopf modules dimodules and doi hopf modules some of them give new examples of rota baxter algebras

integrals for monoidal hom hopf algebras and their applications integrals of monoidal hom hopf algebras are introduced and the existence and uniqueness of integrals for finite dimensional monoidal hom hopf algebras are investigated first then integrals are applied to the maschke type theorem for monoidal hom hopf algebras controlling the semisimplicity and separability of monoidal hom hopf algebras further monoidal hom algebras are characterized with additional frobenius property and the question when finite dimensional monoidal hom hopf algebras are frobenius is studied as applications of integrals the maschke type theorem for hom smash product is given and the morita context in the hom category h mk is constructed

existence and asymptotic behavior of measure valued solutions for degenerate conservation laws abstract we consider two classes of typical degenerate hyperbolic systems of conservation laws to provide a general approach for solving the existence and large time asymptotic behavior of measure valued solutions for initial boundary value problems some existence theorems of the measure valued solutions are established the convergence of large time averages of the measure valued solutions to a dirac mass concentrated at the input state on the boundary is proved for almost each fixed space variable although the measure valued solutions of the initial boundary problems may not be unique in general our results indicate that the asymptotic equilibrium of these measure valued solutions is unique

residual based stabilized higher order fem for advection dominated problems abstract we reconsider the numerical solution of linear ized advection diffusion reaction problems using higher order finite elements together with stabilized galerkin methods of streamline diffusion type supg and with shock capturing stabilization the analysis improves the a priori analysis in our previous paper t knopp g lube g rapin stabilized finite element methods with shock capturing for advection diffusion problems comput methods appl mech engrg 191 2002 2997 3013 the theoretical results are supported by some numerical experiments

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

the maschke theorem for l r smash products in this paper we give a sufficient and necessary condition for generalized l r smash products or generalized diagonal crossed products to be bialgebras hopf algebras and mainly give a maschke theorem for l r smash products and hence obtain maschke theorems for twisted smash products and diagonal crossed products

space division multiple access with a sum feedback rate constraint on a multiantenna broadcast channel simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput which grows double logarithmically with the number of users the sum rate for channel state information csi feedback however increases linearly with the number of users reducing the effective uplink capacity to address this problem a novel space division multiple access sdma design is proposed where the sum feedback rate is upper bounded by a constant this design consists of algorithms for csi quantization threshold based csi feedback and joint beamforming and scheduling the key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small csi quantization errors such that the sum feedback rate constraint is satisfied despite this constraint the proposed sdma design is shown to achieve a sum capacity growth rate close to the optimal one moreover the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates numerical results show that the proposed sdma design is capable of attaining higher sum capacities than existing ones even though the sum feedback rate is bounded

a maschke type theorem for doi hopf modules and applications abstract we prove a maschke type theorem for doi hopf modules a sufficient condition in order to have a maschke type property is that there exists a normalized integral map for the doi hopf datum in question the results are applied to graded modules and to yetter drinfel d modules as another application a characterization of cosemisimple coalgebras over a field is given

a posteriori error estimates in finite element methods for general friedrichs systems abstract in this paper we develop and analyse a new a posteriori error estimator for general friedrichs systems valid for most classical finite element approximations this error estimator is based on comparison between an appropriate norm of the exact error and the l 2 norm of the residuals of the approximate solution we prove that the estimator is independent of the dimension of the space and of the numerical approximation method used moreover the global majoration and local minoration constants are independent of the shape of the mesh

convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions we prove convergence of a class of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions the result is applied to the discontinuous galerkin method due to cockburn hou and shu

galois extensions for co frobenius hopf algebras abstract forhan infinite dimensional co frobenius hopf algebra over a fieldk andaanh comodule algebra the smash producta h ratis linked to the ring of coinvariantsacohby a morita context we use the morita setting to show that for co frobeniush equivalent conditions fora acohto be galois parallel the case ofhfinite dimensional

fixed rings and integrality abstract in this note we offer some variants of a theorem of pare and schelter on integrality in matrix rings we use these to deduce that a ring r is integral over the fixed subring r g under the action of a finite abelian group g provided g r r we also obtain an integrality version of the bergman isaacs theorem

adaptive streamline diffusion finite element methods for stationary convection diffusion problems adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed the underlying discretization scheme is the shock capturing streamline diffusion method the adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed a priori error estimates are used to show that the algorithms are efficient in a certain sense

stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws we propose a class of finite element schemes for systems of hyperbolic conservation laws that are based on finite element discretizations of appropriate relaxation models we consider both semidiscrete and fully discrete finite element schemes and show that the schemes are stable and when the compensated compactness theory is applicable do converge to a weak solution of the hyperbolic system the schemes use piecewise polynomials of arbitrary degree and their consistency error is of high order we also prove that the rate of convergence of the relaxation system to a smooth solution of the conservation laws is of order o eps

entropy flux splittings for hyperbolic conservation laws part i general framework a general framework is proposed for the derivation and analysis of flux splittings and the corresponding flux splitting schemes for systems of conservation laws endowed with a strictly convex entropy the approach leads to several new properties of the existing flux splittings and to a method for the construction of entropy flux splittings for general situations a large family of genuine entropy flux splittings is derived for several significant examples the scalar conservation laws the p system and the euler system of isentropic gas dynamics in particular for the isentropic euler system we obtain a family of splittings that satisfy the entropy inequality associated with the mechanical energy for this system it is proved that there exists a unique genuine entropy flux splitting that satisfies all of the entropy inequalities which is also the unique diagonalizable splitting this splitting can be also derived by the so called kinetic formulation simple and useful difference schemes are derived from the flux splittings for hyperbolic systems such entropy flux splitting schemes are shown to satisfy a discrete cell entropy inequality for the diagonalizable splitting schemes an a priori l estimate is provided by applying the principle of bounded invariant regions the convergence of entropy flux splitting schemes is proved for the 2 2 systems of conservation laws and the isentropic euler system 1995 john wiley sons inc

finite volume schemes for locally constrained conservation laws this paper is devoted to the numerical analysis of the road traffic model proposed by colombo and goatin j differ equ 234 2 654 675 2007 the model involves a standard conservation law supplemented by a local unilateral constraint on the flux at the point x 0 modelling a road light a toll gate etc we first show that the problem can be interpreted in terms of the theory of conservation laws with discontinuous flux function as developed by adimurthi et al j hyperbolic differ equ 2 4 783 837 2005 and burger et al siam j numer anal 47 3 1684 1712 2009 we reformulate accordingly the notion of entropy solution introduced by colombo and goatin j differ equ 234 2 654 675 2007 and extend the well posedness results to the l framework then starting from a general monotone finite volume scheme for the non constrained conservation law we produce a simple scheme for the constrained problem and show its convergence the proof uses a new notion of entropy process solution numerical examples modelling a green wave are presented

an error estimate for finite volume methods for multidimensional conservation laws in this paper an l ll error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained these methods can be formally high order accurate and are defined on general triangulations the error is proven to be of order ft 4 where h represents the size of the mesh via an extension of kuznetsov approximation theory for which no estimate of the total variation and of the modulus of con tinuity in time are needed the result is new even for the finite volume method constructed from monotone numerical flux functions

a new convergence proof for finite volume schemes using the kinetic formulation of conservation laws we give a new convergence proof for finite volume schemes approximating scalar conservation laws the main ingredients of the proof are the kinetic formulation of scalar conservation laws a discrete entropy inequality and the velocity averaging technique

on the structure of tame graded basic hopf algebras ii abstract in this paper firstly we give a complete list of tame local graded frobenius algebras then by the method of bosonization and this list we determine the structure of tame radically graded basic hopf algebras completely

on the stability of finite element methods for shock waves this paper we study the large time asymptotic stability of solutions for systems of nonlinear viscous conservation laws of the form 1 1 u t f u x u xx x 2 r i t 0 u 2 r i u delta 0 u 0 delta we treat systems which are strictly hyperbolic such systems possess a smooth travelling wave solution which is called a viscous p shock wave solution u x t oe x gamma oet x sigma1 oe x u sigma provided that the shock strength ffl j ju gamma u gamma j is small 19 the constant states u sigma and the wave speed oe are related by the rankine hugoniot condition 1 3a f u gamma gamma f u oe u gamma gamma u

skew group algebras in the representation theory of artin algebras then the corresponding crossed product algebra i g or i x g for short has an elements cgieg gi a li i addition is componentwise and multiplication is given by g a g and g g2 y g g2 m in this paper we assume that the values of y lie in the center z a of i hence the action of g on i is given by a group homomorphism g p aut i and 3 can be left out in the special case that y is the trivial map we write 1g instead of i g and the elements as c c li gi ag is then called a skew group ring there is a lot of literature on skew group algebras and crossed product algebras and on the relationship with the ring ac whose elements are those elements of a left fixed by g much work has been done on which properties of li are inherited by n g or ac some of the work on the relationship between these rings has its roots in trying to develop a galois theory for noncommutative rings we refer to 3 7 13 15 19 21 23 25 27 281 and their references in this paper we study these constructions when i is an artin algebra and g a finite group of order n such that n is invertible in 1 under these assumptions the construction preserves central properties of interest in the

duality theorems for rings with actions or coactions graded for s a ring on which g acts as a group of automorphisms let a be s g the skew group ring then from our morita context we obtain g s g z mg s fi where mg is the ring of matrices over s with rows and columns indexed by g and with only finitely many nonzero entries note that if s is a field then mg s sn is dense in end s g with the finite discrete topology s j to obtain our second duality theorem namely that for

a duality theorem for hopf module algebras let g be a locally compact abelian group acting continuously on a von neumann algebra a via a homomorphism ci of g into aut a in 1973 takesaki showed how an action oi of the dual group g could be naturally defined on the von neumann algebra crossed product d x g and proved that the double crossed product 4 x a g x ti g was naturally isomorphic to where 6 is the ring of all bounded operators on l g this duality theorem for group actions was extended to arbitrary locally compact groups g independently by nakagami landstad and stratilavoiculescu zsido in the mid 1970s this extension required replacing the action of g on x r g by a coaction of g on x a g indeed coactions of g are defined in general and it is proved that jl e x rr g x d g n y 0 6 for any action c of g on and corresponding coaction oi of g on x g a similar theorem is proved reversing the roles of c1 and oi an exposition of this theorem may be found in nakagami takesaki 7 where complete references to the literature may also be found nakagami and takesaki phrase things in a dual fashion to handle the topological subtleties more easily in 2 cohen and montgomery recognized that for finite groups g a coaction of g on an f algebra a where f is a field is just a g grading of a it was known that a g grading of an algebra a is the same as an fg module algebra action of fg the hopf algebra dual to fg on a given these facts they were able to prove the following duality theorems

semisimple extensions and elements of trace 1 let h be a hopf algebra which is frobenius over a commutative ring k let a be an h module algebra a h its ring of invariants under the h action and a h the associated semidirect or smash product this setup has been shown by the authors and s montgomery cf cfm to give rise to a morita context ah a a a h with structure maps a aha a h and a a ah thecomodule theoretic concept of h galois extensions was shown cfm under these circumstance to be equivalent to surjectivity of 1 in this paper we start out by showing that another important comodule theoretic concept that of a total integral dl can be translated to a module theoretic concept as well we show that existence of a total integral is equivalent to the surjectivity of which we also termed suggestively existence of an element c e a of trace 1 furthermore if this element c centralizes ah then ah is an ah bimodule direct summand of a we apply these to the morita context associated with the h module algebra a h to prove the main theorem of this paper theorem 1 8 this theorem deals with semisimple extensions sometimes coined maschke type theorems or better yet with separable extensions we show that when a ah is h galois

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

homogenization of linear and nonlinear transport equations we study the homogenization of the linear and nonlinear transport equations with oscillatory velocity fields two types of homogenized equations are derived for general n dimensional linear and nonlinear problems we derive homogenized equations by introducing additional independent variables to represent the small scales for the two dimensional linear transport equations we derive effective equations for the averaged quantities such equations take the form of either a degenerate non local diffusion equation with memory or a higher order hyperbolic equation to study the nonlinear transport equations we introduce the concept of two scale young measure and extend diperna s method to prove that it reduces to a family of dirac measures

a finite element multiresolution viscosity method for hyperbolic conservation laws it is well known that the classic galerkin finite element method is unstable when applied to hyperbolic conservation laws such as the euler equations for compressible flow it is also well known that naively adding artificial diffusion to the equations stabilizes the method but sacrifices too much accuracy to be of any practical use an elegant approach referred to as spectral viscosity methods has been developed for spectral methods in which one adds diffusion only to the high frequency modes of the solution the result being that stabilization is effected without sacrificing accuracy we extend this idea into the finite element framework by using hierarchical finite element functions as a multifrequency basis the result is a new finite element method for solving hyperbolic conservation laws in which artificial diffusion can be applied selectively only to the high frequency modes of the approximation as for spectral viscosity methods this results in stability without compromising accuracy in the context of a one dimensional scalar hyperbolic conservation law we prove the convergence of approximate solutions obtained using the new method to the entropy solution of the conservation law to illustrate the method the results of a computational experiment for a one dimensional hyperbolic conservation law are provided

theory of braided hopf crossed products abstract we define a type of crossed product over braided hopf algebras which generalizes the ones introduced by blattner cohen and montgomery and doi and takeuchi and we study some of its properties for instance we prove maschke s theorem for these new crossed products and we construct a natural morita context which extends the one obtained by cohen fischman and montgomery

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

hopf algebra actions abstract finite groups acting on rings by automorphisms and group graded rings are instances of hopf algebras h acting on h module algebras a we study such actions let a h a a h a e h a all h h the ring of h invariants and form the smash product a h we study the ring extensions ah a a h we prove a maschke type theorem for a h modules we form an associated morita context ah a a a h and use these to get connections between the various rings

convergence of an implicit spacetime godunov finite volume method for a class of hyperbolic systems we study an implicit spacetime godunov method for a class of hyperbolic conservation laws known as temple class systems we establish the well posedness of this method a discrete entropy inequality a property analogous to the total variation diminishing property of certain numerical schemes for scalar conservation laws and as a consequence the convergence of the numerical method

constants of lie algebra actions let r be an associative algebra over a field k and let l be a lie algebra over k acting on r as derivations we will be interested in studying the relationship between r and the ring of constants rl our situation is a special case of the study of rings of invariants of hopf algebra actions and is also analogous to another special case of hopf algebra actions namely the study of fixed rings of finite group actions many of the results in this paper are analogs of results on group actions and give rise to more general questions regarding hopf algebra actions in section 1 we study actions on non nilpotent algebras we first show that any algebraic derivation has non zero constants and then prove that any finite dimensional nilpotent lie algebra of algebraic derivations must act with non zero constants it then follows as a corollary that any finite dimensional nilpotent restricted lie algebra must act with non zero constants these are analogs of results on groups proved in 12 5 in section 2 we prove a necessary condition for the existence of nonzero invariants of certain hopf algebra actions we then use this result to prove the converse of our theorem on nilpotent restricted lie algebras we conclude the section with several questions on general hopf algebra actions

entropy viscosity method for nonlinear conservation laws a new class of high order numerical methods for approximating nonlinear conservation laws is described entropy viscosity method the novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand this new approach does not use any flux or slope limiters applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation various benchmark problems are solved with finite elements spectral elements and fourier series to illustrate the capability of the proposed method

sum discrete rate maximization with rate and power control in layered space time coding this paper generalizes the information theoretic optimality of minimum mean square error successive interference cancellation in layered space time coding with rate and power control based on this derivation a new concept relying on partial feedback is introduced whose core idea is to exploit an additional degree of freedom relative to the partitioning of transmit antennas taking into account this additional degree of freedom together with power control and decoding order allows the reduction of the quantization noise induced by the use of finite discrete rate sets at the transmitter however the simultaneous optimization of all those degrees of freedom proves to be computationally intensive and would result in a tremendous feedback load practical algorithms are thus proposed to achieve this optimization with a reasonable complexity and a limited amount of feedback monte carlo simulations show that those algorithms perform close to the theoretical limits

coupling techniques for nonlinear hyperbolic equations iv well balanced schemes for scalar multi dimensional and multi component laws this series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations the coupling across an interface in the physical space is formulated in term of an augmented system of partial differential equations in an earlier work this strategy allowed us to develop a regularization method based on a thick interface model in one space variable for coupling scalar equations in the present paper we significantly extend this framework and in addition encompass equations in several space variables this new formulation includes the coupling of several distinct scalar conservation laws and allows for a possible covering in space our main contributions are on one hand the design and analysis of a well balanced finite volume method on general triangulations and on the other hand a proof of convergence of this method toward entropy solutions extending coquel cockburn and lefloch s theory restricted to a single conservation law without coupling the core of our analysis is first the derivation of entropy inequalities as well as a discrete entropy dissipation estimate and second a proof of convergence toward the entropy solution of the coupling problem

convergence of a residual based artificial viscosity finite element method we present a residual based artificial viscosity finite element method to solve conservation laws the galerkin approximation is stabilized by only residual based artificial viscosity without any least squares supg or streamline diffusion terms we prove convergence of the method applied to a scalar conservation law in two space dimensions toward an unique entropy solution for implicit time stepping schemes

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

measure valued solutions of scalar conservation laws with boundary conditions we define a solution concept for measure valued solutions to scalar conservation laws with initial conditions and boundary conditions and prove a uniqueness theorem for such solutions this result may be used to prove convergence towards the unique solution for approximate solutions which are uniformly bounded in l weakly consistent with certain entropy inequalities and strongly consistent with the initial condition i e without using derivative estimates as an example convergence of a finite element method is demonstrated

a new version of the two dimensional lax friedrichs scheme we develop a new two dimensional version of the lax friedrichs scheme which corresponds exactly to a transport projection method the scheme we obtain in this way is different from the one derived by averaging the one dimensional scheme in the two directions as usually done the laxfriedrichs scheme is known to be a very stable scheme with much diffusion however this diffusion can be easily reduced by using corrected fluxes without altering the total variation estimates the accuracy of this corrected scheme is of order two except near a local extrema the numerical results computed by using this corrected scheme are similar to the ones obtained by using the godunov scheme with corrected fluxes but require less cpu time convergence towards the entropy solution is proved and some extensions to systems of conservation laws or three dimensional models are discussed some numerical experiments are reported

adaptive finite element methods for conservation laws based on a posteriori error estimates we prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension and design corresponding adaptive methods the proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem together with the galerkin orthogonality of the finite element method the strong stability estimate uses the entropy condition for the system in an essential way 1995 john wiley sons inc

separable functors for the category of doi hopf modules applications abstract we prove a maschke type theorem for the category of doi hopf modules in fact we give necessary and sufficient conditions for the functor that forgets the c coaction to be separable this leads to a generalized notion of integrals our results can be applied to obtain maschke type theorems for yetter drinfel d modules long dimodules and modules graded by g sets existing maschke type theorems due to doi and the authors are recovered as special cases

a conservative nodal variational multiscale method for lagrangian shock hydrodynamics abstract a new method based on a continuous piece wise linear approximation of the equations for lagrangian shock hydrodynamics is presented numerical instabilities are controlled by a stabilizing operator derived using the paradigm of the variational multiscale analysis encouraging numerical comparisons with existing methods in the case of quadrilateral and hexahedral elements indicate that the proposed method is capable of preventing hourglass patterns in the solution while maintaining accuracy in regions of smooth flow the proposed approach satisfies galilean invariance properties and hinges upon the interpretation of the lagrangian shock hydrodynamics equations as a system of nonlinear wave equations a specific implementation in terms of a predictor multi corrector version of the mid point time integrator guarantees global conservation of mass momentum and total energy for each iterate stability and formal order of accuracy are investigated applying the von neumann analysis to the linearized shock hydrodynamics equations in one dimension this approach yields tight bounds for stable time step estimation formal second order accuracy of the method in time and space and valuable indications on the choice of the most appropriate values for the stabilization parameters present in the formulation

stability analysis of explicit entropy viscosity methods for non linear scalar conservation equations this material is based upon work supported by the department of homeland security under agreement 2008 dn 077 ari018 02 national science foundation grants dms 0811041 dms 0914977 dms 1015984 af office of scientific research grant fa99550 12 0358 and is partially supported by award kus c1 016 04 made by king abdullah university of science and technology kaust

upwind finite volume schemes for weakly coupled hyperbolic systems of conservation laws in 2d systems of nonlinear hyperbolic conservation laws in two space dimensions are considered which are characterized by the fact that the coupling of the equations is only due to source terms to solve these weakly coupled systems numerically a class of explicit and implicit upwind finite volume methods on unstructured grids is presented provided an unique entropy solution of the system of conservation laws exists we prove that the approximations obtained by these schemes converge for vanishing discretization parameter to this entropy solution these results are applied to examples from combustion theory and hydrology where the existence of entropy solutions can be shown the proofs rely on an extension of a result due to diperna concerning measure valued solutions to the case of weakly coupled hyperbolic systems

adaptive streamline diffusion methods for compressible flow using conservation variables we consider the streamline diffusion finite element method applied to compressible flow using conservation variables we propose some adaptive algorithms and present related numerical results

a priori error estimates for numerical methods for scalar conservation laws part i the general approach we construct a general theory of a priori error estimates for scalar conservation laws by suitably modifying the original kuznetsov approximation theory as a first application of this general technique we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution thus we obtain optimal error estimates for the engquist osher scheme without using the fact i that the solution is uniformly bounded ii that the scheme is total variation diminishing and iii that the discrete semigroup associated with the scheme has the l 1 contraction property which guarantees an upper bound for the modulus of continuity in time of the approximate solution

numerical viscosity and convergence of finite volume methods for conservation laws with boundary conditions the authors study the convergence of finite volume schemes for general multidimensional conservation laws with boundary conditions a unique result for a measure valued solution which generalizes those of diperna for unbounded domains and szepessy for bounded domains is proved it gives us sufficient conditions to get convergence by studying carefully the entropy production for one dimensional e schemes we are able to prove convergence of finite volume e schemes under general assumption

streamline diffusion finite element method for quasilinear elliptic problems we extend the analysis of the streamline diffusion finite element method to quasilinear elliptic problems of second order an existence theorem and error estimates are given in the case of branches of nonsingular solutions following a recent abstract approach in 12 13 26

a new class of iterative equalizers for space time bicm over mimo block fading multipath awgn channel this paper addresses the issue of advanced equalization methods for space time communications over multiple input multiple output block fading channel with intersymbol interference instead of resorting to conventional multiuser detection techniques based on the straightforward analogy between antennas and users we adopt a different point of view and separate time equalization from space equalization thus introducing a higher degree of freedom in the overall space time equalizer design time domain equalization relies on minimum mean square error criterion and operates on multidimensional modulation symbols whose individual components can be detected in accordance with another criterion in particular when the optimum maximum a posteriori criterion is chosen substantial performance gains over conventional space time turbo equalization have been observed for different transmission scenarios at the price of an increased albeit manageable computational complexity

from finite differences to finite elements a short history of numerical analysis of partial differential equations abstract this is an account of the history of numerical analysis of partial differential equations starting with the 1928 paper of courant friedrichs and lewy and proceeding with the development of first finite difference and then finite element methods the emphasis is on mathematical aspects such as stability and convergence analysis