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

被引：8
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
收藏
页码：1402 / 1423
页数：22
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