Some Recent Developments in Superconvergence of Discontinuous Galerkin Methods for Time-Dependent Partial Differential Equations

被引：0

作者：

Waixiang Cao

Zhimin Zhang

机构：

[1] Beijing Normal University,School of Mathematical Science

[2] Beijing Computational Science Research Center,Department of Mathematics

[3] Wayne State University,undefined

来源：

Journal of Scientific Computing | 2018年 / 77卷

关键词：

Discontinuous Galerkin (DG) method; LDG; Direct discontinuous Galerkin (DDG) method; Superconvergence; Cell average;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we briefly review some recent developments in the superconvergence of three types of discontinuous Galerkin (DG) methods for time-dependent partial differential equations: the standard DG method, the local discontinuous Galerkin method, and the direct discontinuous Galerkin method. A survey of our own results for various time-dependent partial differential equations is presented and the superconvergence phenomena of the aforementioned three types of DG solutions are studied for: (i) the function value and derivative approximation at some special points, (ii) cell average error and supercloseness.

引用

页码：1402 / 1423

页数：21

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