典型文献
A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schr?dinger Equations
文献摘要：
In this paper,we consider the local discontinuous Galerkin method with generalized alter-nating numerical fluxes for two-dimensional nonlinear Schr?dinger 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 Schr?dinger 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.
文献关键词：
中图分类号：
作者姓名：
Hongjuan Zhang;Boying Wu;Xiong Meng
作者机构：
School of Mathematics,Harbin Institute of Technology,Harbin 150001,China;School of Mathematics and Institute for Advanced Study in Mathematics,Harbin Institute of Technology,Harbin 150001,China
文献出处：
引用格式：
[1]Hongjuan Zhang;Boying Wu;Xiong Meng-.A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schr?dinger Equations)[J].应用数学与计算数学学报,2022(01):84-107
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Carte
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