典型文献
Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Methods for KdV Type Equations
文献摘要：
In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving meshes.Based on the L2 conservation law of KdV equations,we adopt the conservative and dissipa-tive numerical fluxes for the nonlinear convection and linear dispersive terms,respectively.Thus,one conservative and three dissipative ALE-DG schemes are proposed for the equa-tions.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 paper.In addition,the L2-norm error estimates are also proved for two schemes,whose numerical fluxes for the linear dispersive term are both dissipative type.More pre-cisely,when choosing the approximation space with the piecewise kth degree polynomials,the error estimate provides the kth order of convergence rate in L2-norm for the scheme with the conservative numerical fluxes applied for the nonlinear convection term.Furthermore,the(k+1/2)th order of accuracy can be proved for the ALE-DG scheme with dissipative numerical fluxes applied for the convection term.Moreover,a Hamiltonian conservative ALE-DG scheme is also presented based on the conservation of the Hamiltonian for KdV equations.Numerical examples are shown to demonstrate the accuracy and capability of the moving mesh ALE-DG methods and compare with stationary DG methods.
文献关键词：
中图分类号：
作者姓名：
Xue Hong;Yinhua Xia
作者机构：
School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,Anhui,China
文献出处：
引用格式：
[1]Xue Hong;Yinhua Xia-.Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Methods for KdV Type Equations)[J].应用数学与计算数学学报,2022(02):530-562
A类：
dissipa,kth
B类：
Arbitrary,Lagrangian,Eulerian,Discontinuous,Galerkin,Methods,KdV,Type,Equations,In,this,paper,several,arbitrary,discontinuous,ALE,DG,methods,presented,Korteweg,Vries,type,equations,moving,meshes,Based,L2,conservation,law,adopt,conservative,numerical,fluxes,nonlinear,convection,dispersive,terms,respectively,Thus,one,three,dissipative,schemes,proposed,invariant,preserving,property,corresponding,properties,other,all,proved,addition,norm,error,estimates,also,two,whose,both,cisely,when,choosing,approximation,space,piecewise,degree,polynomials,provides,order,convergence,applied,Furthermore,k+1,accuracy,can,be,Moreover,Hamiltonian,Numerical,examples,shown,demonstrate,capability,compare,stationary
AB值：
0.425603
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