High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

被引：4

作者：

Zhang, Min ^{[1
]}

Liu, Yang ^{[2
]}

Li, Hong ^{[2
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[2] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China

来源：

COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 2卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Two-dimensional nonlinear fractional diffusion equation; High-order LDG method; Second-order theta scheme; Stability and error estimate; 65M60; 65N30; FINITE-ELEMENT-METHOD; DIFFERENCE APPROXIMATIONS; SPECTRAL METHOD; SUPERCONVERGENCE;

D O I：

10.1007/s42967-019-00058-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, some high-order local discontinuous Galerkin (LDG) schemes based on some second-order theta approximation formulas in time are presented to solve a two-dimensional nonlinear fractional diffusion equation. The unconditional stability of the LDG scheme is proved, and an a priori error estimate with O(hk+1+Delta t2) is derived, where k0 denotes the index of the basis function. Extensive numerical results with Qk(k=0,1,2,3) elements are provided to confirm our theoretical results, which also show that the second-order convergence rate in time is not impacted by the changed parameter theta.

引用

页码：613 / 640

页数：28

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