Weak discrete maximum principle and L∞ analysis of the DG method for the Poisson equation on a polygonal domain

被引：0

作者：

Chiba, Yuki ^{[1
]}

Saito, Norikazu ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Komaba 3-8-1, Tokyo 1538914, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2019年 / 36卷 / 03期

关键词：

Discontinuous Galerkin method; Pointwise error estimate; Maximum principle; DISCONTINUOUS GALERKIN METHODS; FINITE-ELEMENT-METHOD; PENALTY;

D O I：

10.1007/s13160-019-00365-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive several L infinity error estimates for the symmetric interior penalty discontinuous Galerkin method applied to the Poisson equation in a two-dimensional polygonal domain. Both local and global estimates are examined. The weak maximum principle (WMP) for the discrete harmonic function is also established. We prove our L infinity estimates using this WMP and several W-2,W-p and W(1,1)estimates for the Poisson equation. Numerical examples to validate our results are also presented.

引用

页码：809 / 834

页数：26

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