Superconvergence of Energy-Conserving Discontinuous Galerkin Methods for Linear Hyperbolic Equations

查看全文 作　　者：Yong [1]Liu;Chi-Wang [2]Shu;Mengping [1]Zhang

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China;[2]Division of Applied Mathematics,Brown University,Providence,RI 02912,USA

出　　处：《Communications on Applied Mathematics and Computation》索引2019年第1卷第1期,共16页

摘　　要：In this paper,we study the superconvergence properties of the energy-conserving discontinuous Galerkin(DG)method in[18]for one-dimensional linear hyperbolic equations.We prove the approximate solution superconverges to a particular projection of the exact solution.The order of this superconvergence is proved to be k+2 when piecewise Pk polynomials with K≥1 are used.The proof is valid for arbitrary non-uniform regular meshes and for piecewise polynomials with arbitrary K≥1.Furthermore,we find that the derivative and function value approxi?mations of the DG solution are superconvergent at a class of special points,with an order of k+1 and R+2,respectively.We also prove,under suitable choice of initial discretization,a(2k+l)-th order superconvergence rate of the DG solution for the numerical fluxes and the cell averages.Numerical experiments are given to demonstrate these theoretical results. 关键词：Energy-conserving DISCONTINUOUS GALERKIN methods SUPERCONVERGENCE Linear HYPERBOLIC equations

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Superconvergence of Energy-Conserving Discontinuous Galerkin Methods for Linear Hyperbolic Equations

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