boundary effect on asymptotic behaviour of solutions to the p system with linear damping we consider the asymptotic behaviour of solutions to the p system with linear damping on the half line r 0 vt ux 0 ut p v x u with the dirichlet boundary condition u x 0 0 or the neumann boundary condition ux x 0 0 the initial date v0 u0 x has the constant state v u at x l hsiao and t p liu commun math phys 143 1992 599 605 have shown that the solution to the corresponding cauchy problem behaves like diffusion wave and k nishihara j differential equations131 1996 171 188 137 1997 384 395 has proved its optimal convergence rate our main concern in this paper is the boundary effect in the case of null dirichlet boundary condition on u the solution v u is proved to tend to v 0 as t tends to infinity its optimal convergence rate is also obtained by using the green function of the diffusion equation with constant coefficients in the case of null neumann boundary condition on u v 0 t is conservative and v 0 t v0 0 by virtue of the first equation so that v x t is expected to tend to the diffusion wave v x t connecting v0 0 and v in fact the solution v u x t is proved to tend to v x t 0 in the special case v0 0 v the optimal convergence rate is also obtained however this is not known in the case v0 0 v

implicit high order time marching schemes for the linearized euler equations high order accurate implicit time marching methods are presented for discontinuous galerkin and spectral volume high order accurate spatial discretizations of the linearized euler equations that govern propagation of aeroacoustic disturbances it is found that despite the additional computational time that is required for the solution of the large sparse linear system for the degrees of freedom of high order spectral volume or discontinuous galerkin discretizations implicit methods offer an attractive alternative for practical aeroacoustic computations with these high order methods several explicit and implicit methods for time advancement are tested the advantages of implicit higher order accurate in time methods that involve multiple implicit steps are demonstrated the efficiency and accuracy of time marching methods is evaluated for test problems with exact solutions it is shown that complex domain aeroacoustic predictions can be obtained at a reduced computational cost with the use of high order accurate implicit methods

pseudo time stepping methods for space time discontinuous galerkin discretizations of the compressible navier stokes equations the space time discontinuous galerkin discretization of the compressible navier stokes equations results in a non linear system of algebraic equations which we solve with pseudo time stepping methods we show that explicit runge kutta methods developed for the euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality to evaluate its effectiveness we compare with an implicit explicit runge kutta method which does not suffer from the viscous stability constraint we analyze the stability of the methods and illustrate their performance by computing the flow around a 2d airfoil and a 3d delta wing at low and moderate reynolds numbers

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

numerical dispersion analysis of discontinuous galerkin method with different basis functions for acoustic and elastic wave equations the discontinuous galerkin method dgm has been applied to investigate seismic wave propagation recently however few studies have examined the dispersion property of dgm with different basis functions therefore three common basis functions legendre polynomial lagrange polynomial with equidistant nodes and lagrange polynomial with gauss lobatto legendre gll nodes are employed for numerical approximation the numerical dispersion and anisotropy numerical behavior of acoustic and elastic waves are compared and the numerical errors of different order methods are analyzed the result shows that the dispersion errors for all basis functions reduce generally with increasing interpolation orders but with large differences in different directions specifically the legendre basis function and lagrange basis function with gll nodes have attractive advantages over the lagrange polynomial with equidistant nodes for numerical computation we verify the dispersion properties by theoretical and numerical ana

error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations this article considers a posteriori error estimation and anisotropic mesh refinement for three dimensional laminar aerodynamic flow simulations the optimal order symmetric interior penalty discontinuous galerkin discretization which has previously been developed for the compressible navier stokes equations in two dimensions is extended to three dimensions symmetry boundary conditions are given which allow to discretize and compute symmetric flows on the half model resulting in exactly the same flow solutions as if computed on the full model using duality arguments an error estimation is derived for estimating the discretization error with respect to the aerodynamic force coefficients furthermore residual based indicators as well as adjoint based indicators for goal oriented refinement are derived these refinement indicators are combined with anisotropy indicators which are particularly suited to the discontinuous galerkin dg discretization two different approaches based on either a heuristic criterion or an anisotropic extension of the adjoint based error estimation are presented the performance of the proposed discretization error estimation and adaptive mesh refinement algorithms is demonstrated for 3d aerodynamic flows

a multi scale formulation for compressible turbulent flows suitable for general variational discretization techniques based on the recently introduced variational multi scale vms approach to large eddy simulation les as introduced in t j r hughes l mazzei k e jansen large eddy simulation and the variational multiscale method comput visual sci 3 2001 47 59 s s collis monitoring unresolved scales in multiscale turbulence modeling phys fluids 13 6 2001 1800 1806 we present a vms formulation which can be used in the simulation of compressible flows special attention is given to obtain a vms formulation which is suitable for complex flow domains and general variational discretization techniques a generalization of the favre averaging procedure is introduced such that the formulation resembles the favre filtered navier stokes equations traditionally used in les of compressible flow and no explicit subgrid terms arise in the continuity equation also we show that with the use of discretization methods other than fourier spectral methods the vms projection no longer commutes with differentiation this results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to les

minimax principle for the dirac equation the problem of calculating the eigenvalues of the dirac equation by the finite basis expansion method is studied bounds for the eigenvalues are obtained explaining the numerical results on the spectrum that have been observed previously it is argued that the problem of variational collapse can be avoided by finding the minimum over the wave function large component of the maximum over the wave function small component of the energy functional a numerical example is discussed

the strong relaxation limit of the multidimensional isothermal euler equations we construct global smooth solutions to the multidimensional isothermal euler equations with a strong relaxation when the relaxation time tends to zero we show that the density converges towards the solution to the heat equation

frequency localization duhamel principle and its application to the optimal decay of dissipative systems in low dimensions abstract recently a time decay framework l 2 r n b 2 s r n s 0 has been given by 49 for linearized dissipative hyperbolic systems which allows to pay less attention to the traditional spectral analysis however owing to interpolation techniques those decay results for nonlinear hyperbolic systems hold true only in higher dimensions n 3 and the analysis in low dimensions say n 1 2 was left open we try to give a satisfactory answer in the current work first of all we develop new time decay properties on the frequency localization duhamel principle and then it is shown that the classical solution and its derivatives of fractional order decay at the optimal algebraic rate in dimensions n 1 2 by using a new technique which is the so called piecewise duhamel principle in localized time weighted energy approaches compared to 49 finally as direct applications explicit decay statements are worked out for some relevant examples subjected to the same dissipative structure for instance damped compressible euler equations the thermoelasticity with second sound and timoshenko systems with equal wave speeds

h multigrid for space time discontinuous galerkin discretizations of the compressible navier stokes equations being implicit in time the space time discontinuous galerkin discretization of the compressible navier stokes equations requires the solution of a non linear system of algebraic equations at each time step the overall performance therefore highly depends on the efficiency of the solver in this article we solve the system of algebraic equations with a h multigrid method using explicit runge kutta relaxation two level fourier analysis of this method for the scalar advection diffusion equation shows convergence factors between 0 5 and 0 75 this motivates its application to the 3d compressible navier stokes equations where numerical experiments show that the computational effort is significantly reduced up to a factor 10 w r t single grid iterations

global existence and optimal decay rates for the timoshenko system the case of equal wave speeds abstract we first show the global existence and optimal decay rates of solutions to the classical timoshenko system in the framework of besov spaces due to the non symmetric dissipation the general theory for dissipative hyperbolic systems see 31 cannot be applied to the timoshenko system directly in the case of equal wave speeds we construct global solutions to the cauchy problem pertaining to data in the spatially besov spaces furthermore the dissipative structure enables us to give a new decay framework which pays less attention on the traditional spectral analysis consequently the optimal decay estimates of solution and its derivatives of fractional order are shown by time weighted energy approaches in terms of low frequency and high frequency decompositions as a by product the usual decay estimate of l 1 r l 2 r type is also shown

a staggered semi implicit discontinuous galerkin method for the two dimensional incompressible navier stokes equations in this paper we propose a new spatially high order accurate semi implicit discontinuous galerkin dg method for the solution of the two dimensional incompressible navier stokes equations on staggered unstructured curved meshes while the discrete pressure is defined on the primal grid the discrete velocity vector field is defined on an edge based dual grid the flexibility of high order dg methods on curved unstructured meshes allows to discretize even complex physical domains on rather coarse grids formal substitution of the discrete momentum equation into the discrete continuity equation yields one sparse linear equation system with four non zero blocks per element for only one scalar unknown namely the pressure the method is computationally efficient since the resulting system is not only very sparse but also symmetric and positive definite for appropriate boundary conditions furthermore all the volume and surface integrals needed by the scheme presented in this paper depend only on the geometry and the polynomial degree of the basis and test functions and can therefore be precomputed and stored in a preprocessor stage which leads to savings in terms of computational effort for the time evolution part in this way also the extension to a fully curved isoparametric approach becomes natural and affects only the preprocessing step the method is validated for polynomial degrees up to p 3 by solving some typical numerical test problems and comparing the numerical results with available analytical solutions or other numerical and experimental reference data

a staggered space time discontinuous galerkin method for the three dimensional incompressible navier stokes equations on unstructured tetrahedral meshes in this paper we propose a novel arbitrary high order accurate semi implicit space time discontinuous galerkin method for the solution of the three dimensional incompressible navier stokes equations on staggered unstructured curved tetrahedral meshes as is typical for space time dg schemes the discrete solution is represented in terms of space time basis functions this allows to achieve very high order of accuracy also in time which is not easy to obtain for the incompressible navier stokes equations similarly to staggered finite difference schemes in our approach the discrete pressure is defined on the primary tetrahedral grid while the discrete velocity is defined on a face based staggered dual grid while staggered meshes are state of the art in classical finite difference schemes for the incompressible navier stokes equations their use in high order dg schemes is still quite rare a very simple and efficient picard iteration is used in order to derive a space time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five point block system for the scalar pressure which is conveniently solved with a matrix free gmres algorithm from numerical experiments we find that the linear system seems to be reasonably well conditioned since all simulations shown in this paper could be run without the use of any preconditioner even up to very high polynomial degrees for a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point the resulting system is in addition symmetric and positive definite this allows us to use even faster iterative solvers like the conjugate gradient method the flexibility and accuracy of high order space time dg methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both space and time the proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3d test problems and by comparing the obtained numerical results with available exact analytical solutions or with other numerical or experimental reference data to the knowledge of the authors this is the first time that a space time discontinuous galerkin finite element method is presented for the three dimensional incompressible navier stokes equations on staggered unstructured tetrahedral grids high order staggered space time dg scheme for the 3d incompressible navier stokes equations primal grid based on curved tetrahedra dual grid based on non standard five point hexahedra new discretization of the viscous terms on the main grid using lifting operators on the dual grid very simple space time pressure correction algorithm providing also high order in time all linear systems have maximum sparsity and use the smallest possible optimal five point stencil

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows ii efficient flux quadrature a new and efficient quadrature rule for the flux integrals arising in the space time discontinuous galerkin discretization of the euler equations in a moving and deforming space time domain is presented and analyzed the quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme the local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product gauss quadrature rules are used details of the approximation of the dissipation in the numerical flux are presented which render the scheme consistent and stable the method is successfully applied to the simulation of a three dimensional transonic flow over a deforming wing

analysis of a bdf dgfe scheme for nonlinear convection diffusion problems we deal with the numerical solution of a scalar nonstationary nonlinear convection diffusion equation we employ a combination of the discontinuous galerkin finite element method for the space semi discretization and the k step backward difference formula for the time discretization the diffusive and stabilization terms are treated implicitly whereas the nonlinear convective term is treated by a higher order explicit extrapolation method which leads to the necessity to solve only a linear algebraic problem at each time step we analyse this scheme and derive a priori asymptotic error estimates in the discrete l l 2 norm and the l 2 h 1 seminorm with respect to the mesh size h and time step for k 2 3 numerical examples verifying the theoretical results are presented

the boltzmann equation besov spaces and optimal time decay rates in rxn abstract we prove that k th order derivatives of perturbative classical solutions to the hard and soft potential boltzmann equation without the angular cut off assumption in the whole space r x n with n 3 converge in large time to the global maxwellian with the optimal decay rate of o t 1 2 k n 2 n r in the l x r l v 2 norm for any 2 r these results hold for any 0 n 2 as long as initially f 0 b 2 l v 2 in the hard potential case we prove faster decay results in the sense that if p f 0 b 2 l v 2 and i p f 0 b 2 1 l v 2 for n 2 n 2 2 then the solution decays the global maxwellian in l v 2 l x 2 with the optimal large time decay rate of o t 1 2

asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions under the shizuta kawashima condition we show that these solutions approach constant equilibrium state in the lp norm at a rate o t m 2 1 1 p as t tends to infty for p in min m 2 infty moreover we can show that we can approximate with a faster order of convergence theconservative part of the solution in terms of the linearized hyperbolic operator for m 2 and by a parabolic equation in the spirit of chapman enskog expansion the main tool is given by a detailed analysis of the green function for the linearized problem

complex shift and invert strategies for real matrices abstract when using an iterative method for solving a generalized nonsymmetric eigenvalue problem of the form fu mu where f and m are real banded matrices it is often desirable to work with the shifted and inverted operator b f m 1 m in order to enhance the eigenvalue separation and improve efficiency unfortunately the shift is generally complex and so is the matrix b the question then is whether it is possible to avoid complex arithmetic while preserving any advantages of bandedness of the pair f m for the classical problem where m i and f is banded complex arithmetic can be avoided by using double shifts i e by working with the real matrix bb whose bandwidth is double that of f this satisfactory solution extends to the case where m is diagonal as well in the generalized case the answer to the above question is negative in the sense that complex arithmetic can be avoided only at the expense of losing the advantage of bandedness one solution is to factor the shifted matrix f m in complex arithmetic but employ real arithmetic subsequently in the iterative procedure this paper examines several approaches and discusses their respective merits under various circumstances

discontinuous galerkin method for the solution of a transport level set problem the subject of the paper is the numerical analysis of the transport level set problem discretized by the discontinuous galerkin method without the assumption that the first order nonstationary transport equation contains a reaction term which is used in a standard literature we prove error estimates in the l l 2 norm in the case of the space semidiscretization method of lines and in the case of the space time discontinuous galerkin method in the l 2 l 2 norm numerical experiments support the derived error estimates and show that they are not sharp in the case of the space time discontinuous galerkin method

a low frequency assumption for optimal time decay estimates to the compressible navier stokes equations the global existence issue in critical spaces for compressible navier stokes equations was addressed by danchin invent math 141 579 614 2000 and then developed by charve and danchin arch rational mech anal 198 233 271 2010 chen et al commun pure appl math 63 1173 1224 2010 and haspot arch rational mech anal 202 427 460 2011 in more general lp setting the main aim of this paper is to exhibit more precisely time decay estimates of solutions constructed in the critical regularity framework to the best of our knowledge the low frequency assumption usually plays a key role in the large time asymptotics of solutions which was firstly observed by matsumura and nishida j math kyoto univ 20 67 104 1980 in the l 1 mathbb r d space we now claim a new low frequency assumption for barotropic compressible navier stokes equations which may be of interest in the mathematical analysis of viscous fluids precisely if the initial density and velocity additionally belong to some besov space dot b sigma 1 2 infty mathbb r d with the regularity sigma 1 in 1 d 2 2d p d 2 then a sharp time weighted inequality including enough time decay information can be available where optimal decay exponents for the high frequencies are exhibited the proof mainly depends on some non standard besov product estimates as a by product those optimal time decay rates of lq lr type are also captured in the critical framework

a sharp time weighted inequality for the compressible navier stokes poisson system in the critical l p framework abstract the compressible navier stokes poisson system takes the form of usual navier stokes equations coupled with the self consistent poisson equation which is used to simulate the transport of charged particles under the electrostatic potential force in this paper we focus on the large time behavior of global strong solutions in the l p critical besov spaces inspired by the dissipative effect arising from poisson potential we formulate a new regularity assumption of low frequencies and then establish the sharp time weighted inequality which leads to the optimal time decay estimates of strong solutions indeed we see that the decay of density is faster at the half rate than that of velocity which is a different ingredient in comparison with the situation of compressible navier stokes equations our proof mainly depends on tricky and non classical besov product estimates with respect to various sobolev embeddings

diffusive relaxation limit of classical solutions to the damped compressible euler equations abstract we construct uniform global classical solutions to the damped compressible euler equations on the framework of general besov spaces which includes both the usual sobolev spaces h s r d s 1 d 2 and the critical besov space b 2 1 1 d 2 r d such extension heavily depends on a revision of commutator estimates and an elementary fact that indicates the connection between homogeneous and inhomogeneous chemin lerner spaces furthermore we obtain the diffusive relaxation limit of euler equations towards the porous medium equation by means of aubin lions compactness argument

global solution and large time behavior of the 3d compressible euler equations with damping national natural science foundation of china nsaf 10976026 national natural science foundation of china 11271305

large time behavior of solutions for compressible euler equations with damping in r 3 we consider the long time behavior and optimal decay rates of global strong solutions for the isentropic compressible euler equations with damping in r3 in the present paper when the regular initial data belong to some sobolev space hl r3 b 1 s r3 with l 4 and s 0 1 we show that the density of the system converges to its equilibrium state at the rates 1 t 34 s2 in the l2 norm or 1 t 32 s2 in the l norm respectively the momentum of the system decays at the rates 1 t 54 s2 in the l2 norm or 1 t 2 s2 in the l norm respectively which are shown to be optimal for the compressible euler equations with damping

a weak galerkin finite element method for the navier stokes equations abstract this paper introduces a weak galerkin wg finite element method for the navier stokes equations in the primal velocity pressure formulation optimal order error estimates are established for the corresponding numerical approximations it must be emphasized that the wg finite element method is designed on finite element partitions consisting of arbitrary shape of polygons or polyhedra which are shape regular numerical experiments are presented to support the theoretical results

block locally optimal preconditioned eigenvalue xolvers blopex in hypre and petsc we describe our software package block locally optimal preconditioned eigenvalue xolvers blopex recently publicly released blopex is available as a stand alone serial library as an external package to petsc portable extensible toolkit for scientific computation a general purpose suite of tools developed by argonne national laboratory for the scalable solution of partial differential equations and related problems and is also built into hypre high performance preconditioners a scalable linear solvers package developed by lawrence livermore national laboratory the present blopex release includes only one solver the locally optimal block preconditioned conjugate gradient lobpcg method for symmetric eigenvalue problems hypre provides users with advanced high quality parallel multigrid preconditioners for linear systems with blopex the same preconditioners can now be efficiently used for symmetric eigenvalue problems petsc facilitates the integration of independently developed application modules with strict attention to component interoperability and makes blopex extremely easy to compile and use with preconditioners that are available via petsc we present the lobpcg algorithm in blopex for hypre and petsc we demonstrate numerically the scalability of blopex by testing it on a number of distributed and shared memory parallel systems including a beowulf system sun fire 880 an amd dual core opteron workstation and ibm bluegene l supercomputer using petsc domain decomposition and hypre multigrid preconditioning we test blopex on a model problem the standard 7 point finite difference approximation of the 3 d laplacian with the problem size in the range of 10 5 10 8

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation a new space time discontinuous galerkin finite element method for the solution of the euler equations of gas dynamics in time dependent flow domains is presented the discontinuous galerkin discretization results in an efficient elementwise conservative upwind finite element method which is particularly well suited for local mesh refinement the upwind scheme uses a formulation of the hllc flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated the non linear equations of the space time discretization are solved using a multigrid accelerated pseudo time integration technique with an optimized runge kutta method the linear stability of the pseudo time integration method is investigated for the linear advection equation the numerical scheme is demonstrated with simulations of the flow field in a shock tube a channel with a bump and an oscillating naca 0012 airfoil these simulations show that using the data at the superconvergence points the accuracy of the numerical discretization is o h5 2 in space for smooth subsonic flows both on structured and on locally refined meshes and that the space time adaptation can significantly improve the accuracy and efficiency of the numerical method

the optimal decay estimates on the framework of besov spaces for generally dissipative systems we give a new decay framework for the general dissipative hyperbolic system and the hyperbolic parabolic composite system which allows us to pay less attention to the traditional spectral analysis in comparison with previous efforts new ingredients lie in the high frequency and low frequency decomposition of a pseudo differential operator and an interpolation inequality related to homogeneous besov spaces of negative order furthermore we develop the littlewood paley pointwise energy estimates and new time weighted energy functionals to establish optimal decay estimates on the framework of spatially critical besov spaces for the degenerately dissipative hyperbolic system of balance laws based on the l p mathbb r n embedding and the improved gagliardo nirenberg inequality the optimal l p mathbb r n l 2 mathbb r n 1 leqq p 2 decay rates and l p mathbb r n l q mathbb r n 1 leqq p 2 leqq q leqq infty decay rates are further shown finally as a direct application the optimal decay rates for three dimensional damped compressible euler equations are also obtained

hp multigrid as smoother algorithm for higher order discontinuous galerkin discretizations of advection dominated flows part i multilevel analysis the hp multigrid as smoother algorithm hp mgs for the solution of higher order accurate space time discontinuous galerkin discretizations of advection dominated flows is presented this algorithm combines p multigrid with h multigrid at all p levels where the h multigrid acts as smoother in the p multigrid the performance of the hp mgs algorithm is further improved using semi coarsening in combination with a new semi implicit runge kutta method as smoother a detailed multilevel analysis of the hp mgs algorithm is presented to obtain more insight into the theoretical performance of the algorithm as model problem a fourth order accurate space time discontinuous galerkin discretization of the advection diffusion equation is considered the multilevel analysis shows that the hp mgs algorithm has excellent convergence rates both for steady state and time dependent problems and low and high cell reynolds numbers including highly stretched meshes

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

hyperbolic to parabolic relaxation theory for quasilinear first order systems abstract in this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type in particular we obtain a complete theory for the 2 2 systems of genuinely nonlinear hyperbolic balance laws in 1 d with a strong dissipative term a different method which combines the div curl lemma with accretive operators is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics we also investigate relaxation results for some 2 d cases which include the cattaneo model for nonlinear heat conduction and the compressible euler flow moreover convergence result is also obtained for general semilinear systems in 1 d

numerical null controllability of the 1d linear schrodinger equation abstract this paper deals with the numerical approximation to boundary controls that drive the solution to the 1 d linear schrodinger equation to a prescribed state at a final time using ideas from fursikov and imanuvilov we consider the control that minimizes over the class of admissible controls a functional that involves weighted integrals with weights that blow up at t we will see that this extremal problem is equivalent to a differential problem that is fourth order in space and second order in time adapting some numerical techniques applied by the first author and munch to the heat equation we approximate the variational formulation by introducing appropriate space time finite elements that are c 1 in space and c 0 in time we present two approaches the second one relies on a change of variable which leads to a lower condition number for the stiffness matrix the results of some experiments show the efficiency of these methods

variational space time elements for large scale systems abstract in this paper we introduce a new galerkin based formulation for transient continuum problems governed by partial differential equations in space and time therefore we aim at a direct finite element discretization of the space time suitable for massive parallel analysis of the arising large scale problem the proposed formulation is applied to thermal mechanical and fluid systems as well as to a kuramoto sivashinsky problem representing the general class of higher order formulations in material science using nurbs based shape functions we verify whenever possible the conservation properties of the formulation finally a series of examples demonstrate the applicability to all systems presented in this paper

semi implicit discontinuous galerkin methods for the incompressible navier stokes equations on adaptive staggered cartesian grids in this paper a new high order semi implicit discontinuous galerkin method si dg is presented for the solution of the incompressible navier stokes equations on staggered space time adaptive cartesian grids amr in two and three space dimensions the pressure is written in the form of piecewise polynomials on the main grid which is dynamically adapted within a cell by cell amr framework according to the time dependent main grid different face based spatially staggered dual grids are defined for the piece wise polynomials of the respective velocity components although the resulting adaptive staggered grids are more complex than classical uniform cartesian meshes the numerical scheme can still be written in a rather compact form thanks to the use of a tensor product formulation for the definition of the nodal basis in the d dimensional space d 2 3 all the discrete operators can be efficiently written as a combination of linear one dimensional operators acting in the d space directions separately arbitrary high order of accuracy is achieved in space while a very simple semi implicit time discretization is obtained via an explicit discretization of the nonlinear convective terms and an implicit discretization of the pressure gradient in the momentum equation and of the divergence of the velocity field in the continuity equation the real advantages of the staggered grid arise in the solution of the schur complement associated with the saddle point problem of the discretized incompressible navier stokes equations i e after substituting the discrete momentum equations into the discrete continuity equation this leads to a linear system for only one unknown the scalar pressure indeed the resulting linear pressure system is shown to be symmetric and positive definite in order to avoid a quadratic stability condition for the parabolic terms given by the viscous stress tensor an implicit discretization is also used for the diffusive terms in the momentum equation a particular feature of our staggered dg approach is that the viscous stress tensor is discretized on the dual mesh this corresponds to the use of a lifting operator but on the staggered grid both linear systems for pressure and velocity are very efficiently solved by means of a classical matrix free conjugate gradient method for which fast convergence is observed moreover it should be noticed that all test cases shown in this paper have been performed without the use of any preconditioner due to the explicit discretization of the nonlinear convective terms the final algorithm is stable within the classical cfl type time step restriction for explicit dg methods based on the fluid velocity moreover by using a suitable local time stepping technique based on the ader dg framework each element can use its optimal local time step also within the amr context the new space time adaptive staggered dg scheme has been thoroughly verified for polynomial degrees up to n 9 for a large set of non trivial test problems in two and three space dimensions for which analytical numerical or experimental reference solutions exist the high order of accuracy of the scheme is shown by means of a numerical convergence table obtained by comparing the numerical solution against a smooth analytical solution to the knowledge of the authors this is the first staggered semi implicit dg scheme for the incompressible navier stokes equations on space time adaptive meshes in two and three space dimensions

spectral element method in time for rapidly actuated systems in this paper the spectral element se method is applied in time to find the entire time periodic or transient solution of time dependent differential equations the time periodic solution is computed by enforcing periodicity of the element set of particular interest are periodic forcing functions possessing high frequency content to maintain the spectral accuracy for such forcing functions an h refinement scheme is employed near the semi discontinuity without increasing the number of degrees of freedom time discretization by spectral elements is applied initially to a standard form of a set of linear first order differential equations subject to harmonic excitation and an excitation admitting rapid variation other case studies include the application of the se approach to parabolic and hyperbolic partial differential equations the first order form of these equations is obtained through semi discretization using conventional finite element spectral element and finite difference schemes element clustering h refinement is applied to maintain the high accuracy and efficiency in the region of the forcing function admitting rapid variation the convergence in time of the method is demonstrated in some cases machine precision is obtained with 25 degrees of freedom per cycle finally the method is applied to a weakly nonlinear problem with time periodic solution to demonstrate its future applicability to the analysis of limit cycle oscillations in aeroelastic systems

on the stability of damped timoshenko systems cattaneo versus fourier law we consider hyperbolic timoshenko type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction while exponential stability under the fourier law of heat conduction holds it turns out that the coupling via the cattaneo law does not yield an exponentially stable system this seems to be the first example that a removal of the paradox of infinite propagation speed inherent in fourier s law by changing to the cattaneo law causes a loss of the exponential stability property actually for systems with history the fourier law keeps the exponential stability known for the pure timoshenko system without heat conduction but introducing the cattaneo coupling even destroys this property

computational error analysis of a discontinuous galerkin discretization applied to large eddy simulation of homogeneous turbulence a computational error assessment of large eddy simulation les in combination with a discontinuous galerkin finite element method is presented for homogeneous isotropic decaying turbulence the error landscape database approach is used to quantify the total simulation error that arises from the use of the smagorinsky eddy viscosity model in combination with the galerkin discretization we adopt a modified hllc flux allowing an explicit control over the dissipative component of the numerical flux the optimal dependence of the smagorinsky parameter on the spatial resolution is determined for second and third order accurate galerkin methods in particular the role of the numerical dissipation relative to the contribution from the smagorinsky dissipation is investigated we observed an exchange of dissipation principle in the sense that an increased numerical dissipation implied a reduction in the optimal smagorinsky parameter the predictions based on galerkin discretization with fully stabilized hllc flux were found to be less accurate than when a central discretization with mainly smagorinsky dissipation was used this was observed for both the second and third order galerkin discretization suggesting to emphasize central discretization of the convective nonlinearity and stabilization that mimics eddy viscosity as sub filter dissipation

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

dissipative structure and entropy for hyperbolic systems of balance laws in this paper we introduce an entropy condition for hyperbolic systems of balance laws under this condition we use the chapman enskog expansion to derive the corresponding viscous conservation laws further structural conditions are discussed in order to develop local and global existence theories for the balance laws and viscous conservation laws

an interesting class of partial differential equations this paper presents an observation that under reasonable conditions many partial differential equations from mathematical physics possess three structural properties one of them can be understand as a variant of the celebrated onsager reciprocal relation in modern thermodynamics it displays a direct relation of irreversible processes to the entropy change we show that the properties imply various entropy dissipation conditions for hyperbolic relaxation problems as an application of the observation we propose an approximation method to solve relaxation problems moreover the observation is interpreted physically and verified with eight sets of systems from different fields

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

convergence to the barenblatt solution for the compressible euler equations with damping and vacuum we study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in lp with decay rates to matching barenblatt s profile of the porous medium equation the density function tends to the barenblatt s solution of the porous medium equation while the momentum is described by darcy s law

a staggered semi implicit spectral discontinuous galerkin scheme for the shallow water equations a spatially arbitrary high order semi implicit spectral discontinuous galerkin dg scheme for the numerical solution of the shallow water equations on staggered control volumes is derived and discussed the free surface elevation and the momentum are expressed in terms of the same polynomials that are used as basis and as test functions each unknown is however defined on a different set of control volumes that are spatially staggered with respect to each other a semi implicit time integration yields a stable and efficient mass conservative algorithm the use of a staggered mesh has the advantage that after substitution of the momentum equations into the mass conservation equation only one single block penta diagonal system must be solved for the new free surface location which is a scalar quantity subsequently the new momentum components are directly obtained the staggered semi implicit approach makes the present dg scheme different from other published dg schemes the sparse linear system of the resulting discrete wave equation for the free surface can be conveniently solved by a matrix free gmres algorithm furthermore for the shallow water equations the proposed scheme can be written as a quadrature free method where all surface and volume integrals can be precomputed once and for all on the reference element and assembled into universal matrices and tensors for the special case n 0 the proposed method reduces to a classical semi implicit finite difference scheme the proposed semi implicit scheme is particularly well suited for low froude number flows the method is validated on some typical academic benchmark problems using polynomial degrees of up to n 20

efficient iterative method for solving the dirac kohn sham density functional theory we present for the first time an efficient iterative method to directlysolve the four component dirac kohn sham dks density functional theory due to the existence of the negative energy continuum in the dks operator the existing iterative techniques for solving the kohn sham systems cannot be efficiently applied to solve the dks systems the key component of our method is a novel filtering step f which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient lobpcg method the resulting method dubbed the lobpcg f method is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band the lobpcgf method introduces mild extra cost compared to the standard lobpcg method and can be easily implemented we demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription numerical results for pt2 au2 tlf and bi2se3 indicate that the lobpcg f method is a robust and efficient method for investigating the relativistic effect in systems containing heavy

a space time hybridizable discontinuous galerkin method for incompressible flows on deforming domains we present the first space time hybridizable discontinuous galerkin hdg finite element method for the incompressible navier stokes and oseen equations major advantages of a space time formulation are its excellent capabilities of dealing with moving and deforming domains and grids and its ability to achieve higher order accurate approximations in both time and space by simply increasing the order of polynomial approximation in the space time elements our formulation is related to the hdg formulation for incompressible flows introduced recently in e g n c nguyen j peraire b cockburn a hybridizable discontinuous galerkin method for stokes flow comput methods appl mech eng 199 2010 582 597 however ours is inspired in typical dg formulations for compressible flows which allow for a more straightforward implementation another difference is the use of polynomials of fixed total degree with space time hexahedral and quadrilateral elements instead of simplicial elements we present numerical experiments in order to assess the quality of the performance of the methods on deforming domains and to experimentally investigate the behavior of the convergence rates of each component of the solution with respect to the polynomial degree of the approximations in both space and time

the pointwise estimates of solutions for euler equations with damping in multi dimensions we study the time asymptotic behavior of solutions for the isentropic euler equations with damping in multi dimensions the global existence and pointwise estimates of the solutions are obtained furthermore we obtain the optimal lp 1 p convergence rate of the solution when it is a perturbation of a constant state our approach is based on a detailed analysis of the green function of the linearized system and some energy estimates

convergence rate for compressible euler equations with damping and vacuum we study the asymptotic behavior of l weak entropy solutions to the compressible euler equations with damping and vacuum previous works on this topic are mainly concerned with the case away from the vacuum and small initial data in the present paper we prove that the entropy weak solution strongly converges to the similarity solution of the porous media equations in lp r 2 p with decay rates the initial data can contain vacuum and can be arbitrary large a new approach is introduced to control the singularity near vacuum for the desired estimates

lower bounds for an integral involving fractional laplacians and the generalized navier stokes equations in besov spaces when estimating solutions of dissipative partial differential equations in l p related spaces we often need lower bounds for an integral involving the dissipative term if the dissipative term is given by the usual laplacian lower bounds can be derived through integration by parts and embedding inequalities however when the laplacian is replaced by the fractional laplacian the approach of integration by parts no longer applies in this paper we obtain lower bounds for the integral involving by combining pointwise inequalities for with bernstein s inequalities for fractional derivatives as an application of these lower bounds we establish the existence and uniqueness of solutions to the generalized navier stokes equations in besov spaces the generalized navier stokes equations are the equations resulting from replacing in the navier stokes equations by

space time discontinuous galerkin finite element method for two fluid flows a novel numerical method for two fluid flow computations is presented which combines the space time discontinuous galerkin finite element discretization with the level set method and cut cell based interface tracking the space time discontinuous galerkin stdg finite element method offers high accuracy an inherent ability to handle discontinuities and a very local stencil making it relatively easy to combine with local hp refinement the front tracking is incorporated via cut cell mesh refinement to ensure a sharp interface between the fluids to compute the interface dynamics the level set method lsm is used because of its ability to deal with merging and breakup also the lsm is easy to extend to higher dimensions small cells arising from the cut cell refinement are merged to improve the stability and performance the interface conditions are incorporated in the numerical flux at the interface and the stdg discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative the numerical method is applied to one and two dimensional two fluid test problems using the euler equations

space time discontinuous galerkin method for the compressible navier stokes equations a space time discontinuous galerkin finite element method for the compressible navier stokes equations is presented we explain the space time setting derive the weak formulation and discuss our choices for the numerical fluxes the resulting numerical method allows local grid adaptation as well as moving and deforming boundaries which we illustrate by computing the flow around a 3d delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2d airfoil in rapid pitch up maneuver

a space time discontinuous galerkin method for boussinesq type equations in this work we propose a new high order accurate fully implicit space time discontinuous galerkin dg method for advection diffusion dispersion equations i e for so called korteweg de vries type equations in particular we focus on boussinesq type models for free surface flows which are used for the modeling of water waves that travel in deep water where the classical shallow water equations are not valid any more our method follows the ideas of the local dg method ldg for dispersion equations proposed by yan and shu 2002 who used an explicit runge kutta method to integrate their scheme in time however such explicit time integrators applied to dispersive equations imply a very severe restriction on the time step which has to be taken proportional to the cube of the mesh spacing and which therefore can make even one dimensional computations prohibitively expensive on fine grids for the scalar case and with some simplifying assumptions the scheme presented in this paper can be proven to be unconditionally stable in l2 norm furthermore our method is based directly on a space time finite element formulation which also provides a natural way to discretize third order dispersive terms that contain a mixed space time derivative such terms appear frequently in the context of boussinesq type models for free surface flows we will show numerical convergence studies for linear scalar advection diffusion dispersion equations and furthermore we will also study the convergence of our method using solitary wave solutions of the nonlinear boussinesq type model of madsen murray and sorensen 1991

an efficient hyperbolic relaxation system for dispersive non hydrostatic water waves and its solution with high order discontinuous galerkin schemes abstract in this paper we propose a novel set of first order hyperbolic equations that can model dispersive non hydrostatic free surface flows the governing pde system is obtained via a hyperbolic approximation of the family of non hydrostatic free surface flow models recently derived by sainte marie et al in 1 our new hyperbolic reformulation is based on an augmented system in which the divergence constraint of the velocity is coupled with the other conservation laws via an evolution equation for the depth averaged non hydrostatic pressure similar to the hyperbolic divergence cleaning applied in generalized lagrangian multiplier methods glm for magnetohydrodynamics mhd we suggest a formulation in which the divergence errors of the velocity field are transported with a large but finite wave speed that is directly related to the maximal eigenvalue of the governing pde we then use arbitrary high order accurate ader discontinuous galerkin dg finite element schemes with an a posteriori subcell finite volume limiter in order to solve the proposed pde system numerically the final scheme is highly accurate in smooth regions of the flow and very robust and positive preserving for emerging topographies and wet dry fronts it is well balanced making use of a path conservative formulation of hll type riemann solvers based on the straight line segment path furthermore the proposed ader dg scheme with a posteriori subcell finite volume limiter adapts very well to modern gpu architectures resulting in a very accurate robust and computationally efficient computational method for non hydrostatic free surface flows the new model proposed in this paper has been applied to idealized academic benchmarks such as the propagation of solitary waves as well as to more challenging physical situations that involve wave runup on a shore including wave breaking in both one and two space dimensions in all cases the achieved agreement with analytical solutions or experimental data is very good thus showing the validity of both the proposed mathematical model and the numerical solution algorithm

spectral pollution and how to avoid it this paper devoted to the study of spectral pollution contains both abstract results and applications to some self adjoint operators with a gap in their essential spectrum occuring in quantum mechanics first we consider galerkin basis which respect the decomposition of the ambient hilbert space into a direct sum h ph oplus 1 p h given by a fixed orthogonal projector p and we localize the polluted spectrum exactly this is followed by applications to periodic schrodinger operators pollution is absent in a wannier type basis and to dirac operator several natural decompositions are considered in the second part we add the constraint that within the galerkin basis there is a certain relation between vectors in ph and vectors in 1 p h abstract results are proved and applied to several practical methods like the famous kinetic balance of relativistic quantum mechanics

global existence and optimal time decay estimates of solutions to the generalized double dispersion equation on the framework of besov spaces abstract we investigate the initial value problem for the generalized double dispersion equation in any dimensions inspired by 28 for the hyperbolic system of first order pdes we develop littlewood paley pointwise energy estimates for the dissipative wave equation of high order furthermore with aid of the frequency localization duhamel principle we establish the global existence and optimal decay estimates of solutions in spatially critical besov spaces our results could hold true for any dimensions n 1 indeed the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks

self consistent field calculations using chebyshev filtered subspace iteration the power of density functional theory is often limited by the high computational demand in solving an eigenvalue problem at each self consistent field scf iteration the method presented in this paper replaces the explicit eigenvalue calculations by an approximation of the wanted invariant subspace obtained with the help of well selected chebyshev polynomial filters in this approach only the initial scf iteration requires solving an eigenvalue problem in order to provide a good initial subspace in the remaining scf iterations no iterative eigensolvers are involved instead chebyshev polynomials are used to refine the subspace the subspace iteration at each step is easily five to ten times faster than solving a corresponding eigenproblem by the most efficient eigen algorithms moreover the subspace iteration reaches self consistency within roughly the same number of steps as an eigensolver based approach this results in a significantly faster scf iteration

discontinuous galerkin finite element methods for hyperbolic nonconservative partial differential equations we present space and space time discontinuous galerkin finite element dgfem formulations for systems containing nonconservative products such as occur in dispersed multiphase flow equations the main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form then the formulation must reduce to that for conservative systems standard dgfem formulations cannot be applied to nonconservative systems of partial differential equations we therefore introduce the theory of weak solutions for nonconservative products into the dgfem formulation leading to the new question how to define the path connecting left and right states across a discontinuity the effect of different paths on the numerical solution is investigated and found to be small we also introduce a new numerical flux that is able to deal with nonconservative products our scheme is applied to two different systems of partial differential equations first we consider the shallow water equations where topography leads to nonconservative products in which the known possibly discontinuous topography is formally taken as an unknown in the system second we consider a simplification of a depth averaged two phase flow model which contains more intrinsic nonconservative products

an improved iterative hdg approach for partial differential equations abstract we propose and analyze an iterative high order hybridized discontinuous galerkin ihdg discretization for linear partial differential equations we improve our previous work 45 in several directions 1 the improved ihdg approach converges in a finite number of iterations for the scalar transport equation 2 it is unconditionally convergent for both the linearized shallow water system and the convection diffusion equation 3 it has improved stability and convergence rates 4 we uncover a relationship between the number of iterations and time stepsize solution order meshsize and the equation parameters this allows us to choose the time stepsize such that the number of iterations is approximately independent of the solution order and the meshsize and 5 we provide both strong and weak scalings of the improved ihdg approach up to 16 384 cores a connection between ihdg and time integration methods such as parareal and implicit explicit methods are discussed extensive numerical results for linear and nonlinear pdes are presented to verify the theoretical findings

an accurate moving boundary formulation in cut cell methods a cut cell method for cartesian meshes to simulate viscous compressible flows with moving boundaries is presented we focus on eliminating unphysical oscillations occurring in cartesian grid methods extended to moving boundary problems in these methods cells either lie completely in the fluid or solid region or are intersected by the boundary for the latter cells the time dependent volume fraction lying in the fluid region can be so small that explicit time integration schemes become unstable and a special treatment of these cells is necessary when the boundary moves a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level this causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme this temporally discontinuous alteration is shown to act like an unphysical source term which deteriorates the numerical solution i e it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary we develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut cell method which avoids these discontinuities results for canonical two and three dimensional test cases evidence the accuracy and robustness of the newly developed scheme

a multi dimensional high order dg ale method based on gas kinetic theory with application to oscillating bodies this paper presents a multi dimensional high order discontinuous galerkin dg method in an arbitrary lagrangian eulerian ale formulation to simulate flows over variable domains with moving and deforming meshes it is an extension of the gas kinetic dg method proposed by the authors for static domains x ren et al 2015 22 a moving mesh gas kinetic dg method is proposed for both inviscid and viscous flow computations a flux integration method across a translating and deforming cell interface has been constructed differently from the previous ale type gas kinetic method with piecewise constant mesh velocity at each cell interface within each time step the mesh velocity variation inside a cell and the mesh moving and rotating at a cell interface have been accounted for in the finite element framework as a result the current scheme is applicable for any kind of mesh movement such as translation rotation and deformation the accuracy and robustness of the scheme have been improved significantly in the oscillating airfoil calculations all computations are conducted in a physical domain rather than in a reference domain and the basis functions move with the grid movement therefore the numerical scheme can preserve the uniform flow automatically and satisfy the geometric conservation law gcl the numerical accuracy can be maintained even for a largely moving and deforming mesh several test cases are presented to demonstrate the performance of the gas kinetic dg ale method

global classical solutions for partially dissipative hyperbolic system of balance laws the basic existence theory of kato and majda enables us to obtain local in time classical solutions to generally quasilinear hyperbolic systems in the framework of sobolev spaces in x with higher regularity however it remains a challenging open problem whether classical solutions still preserve well posedness in the case of critical regularity this paper is concerned with partially dissipative hyperbolic system of balance laws under the entropy dissipative assumption we establish the local well posedness and blow up criterion of classical solutions in the framework of besov spaces with critical regularity with the aid of the standard iteration argument and friedrichs regularization method then we explore the theory of function spaces and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous chemin lerner spaces mixed space time besov spaces this fact allows us to capture the dissipation rates generated from the partial dissipative source term and further obtain the global well posedness and stability by assuming at all times the shizuta kawashima algebraic condition as a direct application the corresponding well posedness and stability of classical solutions to the compressible euler equations with damping are also obtained

discontinuous galerkin finite element method for shallow two phase flows we present a discontinuous galerkin finite element method for two depth averaged two phase flow models one of these models contains nonconservative products for which we developed a discontinuous galerkin finite element formulation in rhebergen et al 2008 j comput phys 227 1887 1922 the other model is a new depth averaged two phase flow model we introduce for shallow two phase flows that does not contain nonconservative products we will compare numerical results of both models and qualitatively validate the models against a laboratory experiment furthermore because of spurious oscillations that may occur near discontinuities a weno slope limiter is applied in conjunction with a discontinuity detector to detect regions where spurious oscillations appear

decay structure for symmetric hyperbolic systems with non symmetric relaxation and its application this paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation when the relaxation matrix is symmetric the dissipative structure of the systems is completely characterized by the kawashima shizuta stability condition formulated in umeda et al jpn j appl math 1 435 457 1984 and shizuta and kawashima hokkaido math j 14 249 275 1985 and we obtain the asymptotic stability result together with the explicit time decay rate under that stability condition however some physical models which satisfy the stability condition have non symmetric relaxation term for example the timoshenko system and the euler maxwell system moreover it had been already known that the dissipative structure of such systems is weaker than the standard type and is of the regularity loss type see duan in j hyperbolic differ equ 8 375 413 2011 ide et al in math models meth appl sci 18 647 667 2008 ide and kawashima in math models meth appl sci 18 1001 1025 2008 ueda et al in siam j math anal 2012 ueda and kawashima in methods appl anal 2012 therefore our purpose in this paper is to formulate a new structural condition which includes the kawashima shizuta condition and to analyze the weak dissipative structure for general systems with non symmetric relaxation

entropy and global existence for hyperbolic balance laws this paper presents a general result on the existence of global smooth solutions to hyperbolic systems of balance laws in several space variables we propose an entropy dissipation condition and prove the existence of global smooth solutions under initial data close to a constant equilibrium state in addition we show that a system of balance laws satisfies a kawashima condition if and only if its first order approximation namely the hyperbolic parabolic system derived through the chapman enskog expansion satisfies the corresponding kawashima condition the result is then applied to bouchut s discrete velocity bgk models approximating hyperbolic systems of conservation laws