Arbitrary Lagrangian‑Eulerian Discontinuous Galerkin Methods for KdV Type Equations

作     者：Xue Hong Yinhua Xia Xue Hong;Yinhua Xia

作者机构：School of Mathematical SciencesUniversity of Science and Technology of ChinaHefei 230026AnhuiChina 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2022年第4卷第2期

页      面：530-562页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported by the National Numerical Windtunnel Project NNW2019ZT4-B08 Science Challenge Project TZZT2019-A2.3 the National Natural Science Foundation of China Grant no.11871449 

主　　题：Arbitrary Lagrangian-Eulerian discontinuous Galerkin methods KdV equations Conservative schemes Dissipative schemes Error estimates 

摘      要：In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving *** on the L^(2) conservation law of KdV equations,we adopt the conservative and dissipative numerical fuxes for the nonlinear convection and linear dispersive terms,***,one conservative and three dissipative ALE-DG schemes are proposed for the *** invariant preserving property for the conservative scheme and the corresponding dissipative properties for the other three dissipative schemes are all presented and proved in this *** addition,the L^(2)-norm error estimates are also proved for two schemes,whose numerical fuxes for the linear dispersive term are both dissipative *** precisely,when choosing the approximation space with the piecewise kth degree polynomials,the error estimate provides the kth order of convergence rate in L^(2)-norm for the scheme with the conservative numerical fuxes applied for the nonlinear convection ***,the(k+1∕2)th order of accuracy can be proved for the ALE-DG scheme with dissipative numerical fuxes applied for the convection ***,a Hamiltonian conservative ALE-DG scheme is also presented based on the conservation of the Hamiltonian for KdV *** examples are shown to demonstrate the accuracy and capability of the moving mesh ALE-DG methods and compare with stationary DG methods.