The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law

被引：29

作者：

Li, Changpin ^{[1
]}

Wang, Zhen ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2020年 / 169卷

基金：

中国国家自然科学基金;

关键词：

Caputo derivative; Discontinuous Galerkin method; Stability; Convergence; FRACTIONAL DIFFUSION; RANDOM-WALKS; SUPERCONVERGENCE; ALGORITHM; EQUATIONS; SCHEME; MESHES;

D O I：

10.1016/j.matcom.2019.09.021

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, efficient methods for numerical solutions of Caputo-type nonlinear conservation laws are established and studied, where the time fractional derivative with order in (0, 1) is discretized by the finite difference method and the spatial derivative by the discontinuous Galerkin finite element method. The derived numerical schemes for one and two space dimensions are shown to be stable and convergent. Numerical experiments are provided to support these conclusions. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B. V. All rights reserved.

引用

页码：51 / 73

页数：23

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