L2-ERROR ANALYSIS OF FULLY DISCRETE DISCONTINUOUS GALERKIN APPROXIMATIONS FOR NONLINEAR SOBOLEV EQUATIONS

被引：8

作者：

Ohm, Mi Ray ^{[1
]}

Lee, Hyun Young ^{[2
]}

机构：

[1] Dongseo Univ, Div Informat Syst Engn, Pusan 617716, South Korea

[2] Kyungsung Univ, Dept Math, Pusan 608736, South Korea

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2011年 / 48卷 / 05期

关键词：

nonlinear Sobolev equation; discontinuous Galerkin approxirnation; fully discrete approximations; optimal L-2 error estimates; PARTIAL-DIFFERENTIAL EQUATIONS; PARABOLIC EQUATIONS; CONVERGENCE; TIME;

D O I：

10.4134/BKMS.2011.48.5.897

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal L-2 error estimates.

引用

页码：897 / 915

页数：19

共 50 条

[31] A Fully-Discrete Local Discontinuous Galerkin Method for Convection-Dominated Sobolev Equation
Qiang Zhang
Fuzheng Gao
Journal of Scientific Computing, 2012, 51 : 107 - 134
[32] A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface
Wang, Liang
Yuan, Xinpeng
Xiong, Chunguang
Wu, Huibin
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 390
[33] Optimal Energy Conserving Local Discontinuous Galerkin Methods for Elastodynamics: Semi and Fully Discrete Error Analysis
Ruchi Guo
Yulong Xing
Journal of Scientific Computing, 2021, 87
[34] Optimal Energy Conserving Local Discontinuous Galerkin Methods for Elastodynamics: Semi and Fully Discrete Error Analysis
Guo, Ruchi
Xing, Yulong
JOURNAL OF SCIENTIFIC COMPUTING, 2021, 87 (01)
[35] ERROR ESTIMATES FOR SINGLE STEP FULLY DISCRETE APPROXIMATIONS FOR NONLINEAR SECOND ORDER HYPERBOLIC EQUATIONS.
Bales, L.A.
Computers & mathematics with applications, 1988, 15 (6-8): : 535 - 553
[36] Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection - diffusion and KdV equations
Xu, Yan
Shu, Chi-Wang
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (37-40) : 3805 - 3822
[37] L∞ error estimates of discontinuous Galerkin methods for delay differential equations
Li, Dongfang
Zhang, Chengjian
APPLIED NUMERICAL MATHEMATICS, 2014, 82 : 1 - 10
[38] An optimal-order L2-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic equation in multiple space dimensions
Wang, Kaixin
Wang, Hong
Sun, Shuyu
Wheeler, Mary F.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2009, 198 (27-29) : 2190 - 2197
[39] ERROR-ESTIMATES FOR SINGLE STEP FULLY DISCRETE APPROXIMATIONS FOR NONLINEAR 2ND ORDER HYPERBOLIC-EQUATIONS
BALES, LA
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1988, 15 (6-8) : 535 - 553
[40] Error Estimate of a Fully Discrete Local Discontinuous Galerkin Method for Variable-Order Time-Fractional Diffusion Equations
Leilei Wei
Shuying Zhai
Xindong Zhang
Communications on Applied Mathematics and Computation, 2021, 3 : 429 - 443

← 1 2 3 4 5 →