A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schrödinger Equations

查看全文 作　　者：Hongjuan [1]Zhang;Boying [2]Wu;Xiong [2]Meng

机构地区：[1]School of Mathematics,Harbin Institute of Technology,Harbin 150001,China;[2]School of Mathematics and Institute for Advanced Study in Mathematics,Harbin Institute of Technology,Harbin 150001,China

出　　处：《Communications on Applied Mathematics and Computation》索引2022年第4卷第1期,共24页

基　　金：the National Natural Science Foundation of China Grants U1637208 and 71773024.;the National Natural Science Foundation of China Grant 11971132. 摘　　要：In this paper,we consider the local discontinuous Galerkin method with generalized alter-nating numerical fluxes for two-dimensional nonlinear Schrödinger equations on Carte-sian meshes.The generalized fluxes not only lead to a smaller magnitude of the errors,but can guarantee an energy conservative property that is useful for long time simulations in resolving waves.By virtue of generalized skew-symmetry property of the discontinuous Galerkin spatial operators,two energy equations are established and stability results con-taining energy conservation of the prime variable as well as auxiliary variables are shown.To derive optimal error estimates for nonlinear Schrödinger equations,an additional energy equation is constructed and two a priori error assumptions are used.This,together with properties of some generalized Gauss-Radau projections and a suitable numerical initial condition,implies optimal order of k+1.Numerical experiments are given to demonstrate the theoretical results. 关键词：Local discontinuous Galerkin method Two-dimensional nonlinear Schrödinger equation Generalized alternating fluxes Optimal error estimates

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A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schrödinger Equations

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