high resolution staggered mesh approach for nonlinear hyperbolic systems of conservation laws abstract a numerical technique is presented to approximate weak solutions of hyperbolic systems of conservation laws in one and two space dimensions when strong shocks are present in the exact solution other techniques rely on approximate riemann problem solvers to cope with this difficulty the high order approach here does not use approximate riemann solvers as a building block and is therefore considerably easier to implement compared to the usual methods moreover the approach here yields sharp nonoscillatory shocks sharp corners at the base of rarefaction waves and has high order accuracy in regions where the solution is smooth for the scalar one dimensional problem the theoretical results confirm the reliability of this approach

singular boundary resonance with turning point resonance the resonance criteria of the singularly perturbed equation frac 1 2 varepsilon xp x varepsilon u xx x a x q x varepsilon u x su are investigated on 0 x b with 0 a b and 0 varepsilon ll 1 the matched uniform asymptotic approximations developed by the authors in a companion paper for a singular point and turning point respectively are used to calculate asymptotic approximations for the resonance criteria and the associated eigenvalue problem to exponential precision the eigenvalues can be identified as being dominated by the pure singular point problem the pure turning point problem or by combinations of the two problems an asymptotic exponential precision notation is introduced to succinctly express the resonance criteria given to leading order in varepsilon

resonance for singular perturbation problems consider the resonance for a second order equation ey xpy qy 0 another proof is given for the necessity of the matkowsky condition and the connection with a regular eigenvalue problem is established also if p q are analytic necessary and sufficient conditions are derived

why the muscl hancock scheme is l 1 stable the finite volume methods are one of the most popular numerical procedure to approximate the weak solutions of hyperbolic systems of conservation laws they are developed in the framework of first order numerical schemes several approaches are proposed to increase the order of accuracy the van leer methods are interesting ways one of them namely the muscl hancock scheme is full time and space second order accuracy in the present work we exhibit relevant conditions to ensure the l1 stability of the method a cfl like condition is established and a suitable limitation procedure for the gradient reconstruction is developed in order to satisfy the stability criterion in addition we show that the conservative variables are not useful within the gradient reconstruction and the procedure is extended in the framework of the primitive variables numerical experiments are performed to show the interest and the robustness of the method

global entropy solutions to exothermically reacting compressible euler equations abstract the global existence of entropy solutions is established for the compressible euler equations for one dimensional or plane wave flow of an ideal gas which undergoes a one step exothermic chemical reaction under arrhenius type kinetics we assume that the reaction rate is bounded away from zero and the total variation of the initial data is bounded by a parameter that grows arbitrarily large as the equation of state converges to that of an isothermal gas the heat released by the reaction causes the spatial total variation of the solution to increase however the increase in total variation is proved to be bounded in t 0 as a result of the uniform and exponential decay of the reactant to zero as t approaches infinity

domain decomposition for compressible navier stokes equations with different discretizations and formulations the purpose of this work is to couple different numerical models and approximations for the calculation of high speed external flows governed by the compressible navier stokes equations the proposed coupling is achieved by the boundary conditions which impose viscous fluxes and friction forces on the body for the calculation of the global external flow and which impose dirichlet type boundary conditions on the interface for the local model

coupling boltzmann and navier stokes equations by friction the aim of this paper is to introduce and validate a coupled navier stokes boltzman approach for the calculation of hypersonic rarefied flows around manoeuvering vehicles the proposed strategy uses locally a kinetic model in the boundary layer coupled through wall friction forces to a global navier stokes solver dif ferent numerical experiments illustrate the potentialities of the method

robustness of muscl schemes for 2d unstructured meshes we consider second order accuracy muscl schemes to approximate the solutions of hyperbolic system of conservation laws in the context of the 2d unstructured grids we propose a limitation procedure on the gradient reconstruction to enforce several stability properties we establish that the muscl scheme preserves the invariant domains and satisfy a set of entropy inequalities a conservation assumption is not useful in the present work to define the piecewise linear approximations and the proposed limitation can be understood as a systematic correction of the standard gradient reconstruction procedure the numerical method is applied to the compressible euler equations the gradient reconstruction is performed using the characteristic variables several numerical tests exhibit stability and robustness of the scheme

convergence analysis of a transmission algorithm for convection diffusion problems we prove the convergence of the transmission time marching algorithm for the beta monoscale multimodel methods for hydrodynamics type problems our analysis is based on the author s transmission multiplier method we introduced in c r acad sci paris ser i math 328 1999 pp 637 642 and the local global and trace estimates we developed in j math anal appl 229 1999 pp 137 157 abstr appl anal 3 2001 pp 131 150

dilworth rate a generalization of witsenhausen s zero error rate for directed graphs we investigate a communication setup where a source output is sent through a free noisy channel first and an additional codeword is sent through a noiseless but expensive channel later with the help of the second message the decoder should be able to decide with zero error whether its decoding of the first message was error free this scenario leads to the definition of a digraph parameter that generalizes witsenhausen s zero error rate for directed graphs we investigate this new parameter for some specific directed graphs and explore its relations to other digraph parameters such as sperner capacity and dichromatic number we also look at the natural variant of the above problem where the decoder should decode the first message with zero error not only decide whether its earlier decoding was correct in this case the witsenhausen rate of an appropriately defined undirected graph turns out to be the relevant parameter

a review on singularly perturbed differential equations with turning points and interior layers singular perturbation problems with turning points arise as mathematical models for various physical phenomena the problem with interior turning point represent one dimensional version of stationary convection diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin boundary turning point problems on the other hand arise in geophysics and in modeling thermal boundary layers in laminar flow in this paper we review some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems the purpose is to find out what problems are treated and what numerical asymptotic methods are employed with an eye towards the goal of developing general methods to solve such problems since major work in this area started after 1970 so this paper limits its coverage to the work done by numerous researchers between 1970 and 2011

the zero undetected error capacity approaches the sperner capacity ahlswede cai and zhang proved that in the noise free limit the zero undetected error capacity is lower bounded by the sperner capacity of the channel graph and they conjectured equality here we derive an upper bound that proves the conjecture

graph decomposition a new key to coding theorems a new and simple method is proposed for finding good encoders both for channels and for sources with side information this method relies on the continuous version of a graph decomposition result of lovasz the presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound the previous bounds for universal codes of the authors and marton are also improved

staggered mixed finite volume finite element method for the navier stokes equations to solve flow problems associated with the navier stokes equations we construct a mixed finite volume finite element method for the spatial approximation of the convective and diffusive parts of the flux respectively the finite volume component of the method is adapted from the authors construction for hyperbolic conservation laws and rectangular or unstructured triangular grids of two dimensional finite volume extensions of the lax friedrichs and nessyahu tadmor central difference schemes in which the resolution of riemann problems at cell interfaces is bypassed thanks to the use of the lax friedrichs scheme on two specific staggered grids muscl type piecewise linear cell interpolants slope limiters and a two step predictor corrector time discretization lead to an oscillation free quasi second order resolution for the viscous terms we use a centered finite element approximation inspired by rostand stoufflet to improve the quality of the resolution we use a grid adaptation algorithm proposed by castro diaz and hecht

central schemes for balance laws of relaxation type several models in mathematical physics are described by quasi linear hyperbolic systems with source term and in several cases the production term can become stiff here suitable central numerical schemes for such problems are developed and applications to the broadwell model and extended thermodynamics are presented the numerical methods are a generalization of the nessyahu tadmor scheme to the nonhomogeneous case by including the cell averages of the production terms in the discrete balance equations a second order scheme uniformly accurate in the relaxation parameter is derived and its properties analyzed numerical tests confirm the accuracy and robustness of the scheme

errors and erasures decoding for block codes with feedback inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors and erasures decoding first an inner bound is derived using a two phase encoding scheme with communication and control phases together with the optimal decoding rule for the given encoding scheme among decoding rules that can be represented in terms of pairwise comparisons between the messages then an outer bound is derived using a generalization of the straight line bound to errors and erasures decoders and the optimal error exponent tradeoff of a feedback encoder with two messages in addition upper and lower bounds are derived for the optimal erasure exponent of error free block codes in terms of the rate finally a proof is provided for the fact that the optimal tradeoff between error exponents of a two message code does not improve with feedback on discrete memoryless channels dmcs

a converse coding theorem for mismatched decoding at the output of binary input memoryless channels an upper bound on the maximal transmission rate over binary input memoryless channels provided that the decoding decision rule is given is derived if the decision rule is equivalent to the maximum likelihood decoding matched decoding then the bound coincides with the channel capacity otherwise mismatched decoding it coincides with a known lower bound

convergence analysis of domain decomposition algorithms with full overlapping for the advection diffusion problems the aim of this paper is to study the convergence properties of a time marching algorithm solving advection diffusion problems on two domains using incompatible discretizations the basic algorithm is first presented and theoretical or numerical results illustrate its convergence properties this study is based on spectral theory a priori estimates and a di giorgi nash maximum principle

a numerical study of the axisymmetric couette taylor problem using a fast high resolution second order central scheme we present a numerical study of the axisymmetric couette taylor problem using a finite difference scheme the scheme is based on a staggered version of a second order central differencing method combined with a discrete hodge projection the use of central differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms the result is a simple and efficient scheme which is readily adaptable to other geometries and to more complicated flows the scheme exhibits competitive performance in terms of accuracy resolution and robustness the numerical results agree accurately with linear stability theory and with previous numerical studies

central finite volume methods with constrained transport divergence treatment for ideal mhd two and three dimensional finite volume extensions of the lax friedrichs lf and nessyahu tadmor one dimensional difference schemes were previously presented and successfully applied to several problems for nonlinear hyperbolic systems and in particular to typical test cases for both inviscid and viscous compressible flows these central schemes by pass the resolution at the cell interfaces of the riemann problems thanks to the use of the staggered lf scheme which serves as the base scheme on which high order finite volume methods can be constructed using van leer s muscl type limited reconstruction principle for this purpose two dual grids are used at alternate time steps these methods are extended here to several problems in one and multi dimensional ideal compressible magnetohydrodynamics using a modified version of the first author s central methods with oblique diamond shaped dual cells in two dimensions the system has eight equations and solving the corresponding riemann problem is an elaborate and time consuming process central methods lead to significant computing time reductions and the numerical experiments presented here suggest the accuracy is quite satisfactory in order to satisfy the physical constraint b 0 we have constructed a strategy ctcs inspired from the constrained transport method of evans and hawley the validity of our base scheme and our ctcs approach is clearly confirmed by the results

error estimates for the hybrid finite element finite volume methods for linear hyperbolic and convection dominated problems in this paper we establish the error estimates for the generalized hybrid finite element finite volume methods we have introduced in our earlier work j comput appl math 139 2002 323 comm appl anal 5 1 2001 91 these estimates are obtained for linear hyperbolic and convection dominated convection diffusion problems our analysis is performed for general mesh of a bounded polygonal domain of rn satisfying the minimum angle condition our errors estimates are new and represent significant improvements over the previously known error estimates established for the streamline diffusion and discontinuous galerkin methods applied to hyperbolic and convection dominated problems math comp 46 1986 1 comput methods appl mech eng 45 1984 285 in c de boor ed mathematical aspects of finite elements in partial differential equations academic press new york 1974