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

共 50 条

[31] Discontinuous Galerkin finite element methods for time-dependent Hamilton–Jacobi–Bellman equations with Cordes coefficients
Iain Smears
Endre Süli
Numerische Mathematik, 2016, 133 : 141 - 176
[32] Numerical resolution of discontinuous Galerkin methods for time dependent wave equations
Zhong, Xinghui
Shu, Chi-Wang
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2011, 200 (41-44) : 2814 - 2827
[33] On the efficiency of spectral deferred correction methods for time-dependent partial differential equations
Layton, Anita T.
APPLIED NUMERICAL MATHEMATICS, 2009, 59 (07) : 1629 - 1643
[34] Superconvergence of discontinuous Galerkin solutions for higher-order ordinary differential equations
Temimi, H.
APPLIED NUMERICAL MATHEMATICS, 2015, 88 : 46 - 65
[35] Weak Galerkin methods for time-dependent Maxwell's equations
Shields, Sidney
Li, Jichun
Machorro, Eric A.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (09) : 2106 - 2124
[36] Superconvergence of Energy-Conserving Discontinuous Galerkin Methods for Linear Hyperbolic Equations
Liu, Yong
Shu, Chi-Wang
Zhang, Mengping
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2019, 1 (01) : 101 - 116
[37] Optimal Superconvergence of Energy Conserving Local Discontinuous Galerkin Methods for Wave Equations
Cao, Waixiang
Li, Dongfang
Zhang, Zhimin
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2017, 21 (01) : 211 - 236
[38] AN ADAPTIVE MULTIRESOLUTION DISCONTINUOUS GALERKIN METHOD FOR TIME-DEPENDENT TRANSPORT EQUATIONS IN MULTIDIMENSIONS
Guo, Wei
Cheng, Yingda
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2017, 39 (06): : A2962 - A2992
[39] SUPERCONVERGENCE OF DISCONTINUOUS GALERKIN METHODS FOR LINEAR HYPERBOLIC EQUATIONS WITH SINGULAR INITIAL DATA
Guo, Li
Yang, Yang
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2017, 14 (03) : 342 - 354
[40] Superconvergence of Energy-Conserving Discontinuous Galerkin Methods for Linear Hyperbolic Equations
Yong Liu
Chi-Wang Shu
Mengping Zhang
Communications on Applied Mathematics and Computation, 2019, 1 : 101 - 116

← 1 2 3 4 5 →