Local Discontinuous Galerkin Method for Time-Dependent Singularly Perturbed Semilinear Reaction-Diffusion Problems

被引：4

作者：

Cheng, Yao ^{[1
]}

Song, Chuanjing ^{[1
]}

Mei, Yanjie ^{[2
]}

机构：

[1] Suzhou Univ Sci & Technol, Sch Math Sci, Suzhou, Peoples R China

[2] Suzhou Univ Sci & Technol, Int Educ Sch, Suzhou, Peoples R China

来源：

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2021年 / 21卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Singularly Perturbed; Semilinear Reaction-Diffusion; Local Discontinuous Galerkin Method; Error Estimates; ALTERNATING NUMERICAL FLUX; FINITE-ELEMENT METHODS; ERROR ESTIMATE; LDG METHOD;

D O I：

10.1515/cmam-2019-0185

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Local discontinuous Galerkin method is considered for ime-dependent singularly perturbed semi linear problems with boundary layer. The method is equipped with a general numerical flux including two kinds of independent parameters. By virtue of the weighted estimates and suitably designed global projections, we establish optimal (k + 1)-th error estimate in a local region at a distance of 0(h log(17;)) from domain boundary. Here k is the degree of piecewise polynomials in the discontinuous finite element space and h is the maximum mesh size. Both semi-discrete LDG method and fully discrete LDG method with a third-order explicit Runge Kutta time-marching are considered. Numerical experiments support our theoretical results.

引用

页码：31 / 52

页数：22

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