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

被引：7

作者：

Cao, Waixiang ^{[1
]}

Zhang, Zhimin ^{[2
,3
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing, Peoples R China

[2] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[3] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2018年 / 77卷 / 03期

关键词：

Discontinuous Galerkin (DG) method; LDG; Direct discontinuous Galerkin (DDG) method; Superconvergence; Cell average; FINITE-ELEMENT-METHOD; LINEAR HYPERBOLIC-EQUATIONS; CONVECTION-DIFFUSION EQUATIONS; HIGHER-ORDER DERIVATIVES; ONE SPACE DIMENSION; INTERIOR PENALTY METHOD; CONSERVATION-LAWS; SCHRODINGER-EQUATIONS; SPECTRAL COLLOCATION; PARABOLIC EQUATIONS;

D O I：

10.1007/s10915-018-0762-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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：22

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