Weak Galerkin finite element methods for linear parabolic integro-differential equations

被引：21
作者：
Zhu, Ailing [1 ]
Xu, Tingting [1 ]
Xu, Qiang [1 ]
机构：
[1] Shandong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 32卷 / 05期
基金：
中国国家自然科学基金;
关键词：
error estimates; finite element methods; integro-differential equations; weak Galerkin methods; 2ND-ORDER ELLIPTIC PROBLEMS; BIHARMONIC EQUATION; NUMERICAL-SOLUTION; APPROXIMATIONS;
D O I：
10.1002/num.22053
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The semidiscrete and fully discrete weak Galerkin finite element schemes for the linear parabolic integro-differential equations are proposed. Optimal order error estimates are established for the corresponding numerical approximations in both L 2 and H 1 norms. Numerical experiments illustrating the error behaviors are provided.(c) 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1357-1377, 2016
引用
收藏
页码：1357 / 1377
页数：21
相关论文
共 31 条
[1]  
Adams R.A., 1975, Sobolev Spaces
[2]  
[Anonymous], 1977, MATH ASPECTS FINITE
[3]   H1-Galerkin expanded mixed finite element methods for nonlinear pseudo-parabolic integro-differential equations [J].
Che, Haitao ;
Zhou, Zhaojie ;
Jiang, Ziwen ;
Wang, Yiju .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2013, 29 (03) :799-817
[4]   FINITE-ELEMENT APPROXIMATION OF A PARABOLIC INTEGRODIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL [J].
CHEN, C ;
THOMEE, V ;
WAHLBIN, LB .
MATHEMATICS OF COMPUTATION, 1992, 58 (198) :587-602
[5]   A modified weak Galerkin finite element method for a class of parabolic problems [J].
Gao, Fuzheng ;
Wang, Xiaoshen .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 271 :1-19
[6]   Crank-Nicolson least-squares Galerkin procedures for parabolic integro-differential equations [J].
Guo, Hui ;
Rui, Hongxing .
APPLIED MATHEMATICS AND COMPUTATION, 2006, 180 (02) :622-634
[7]   L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type [J].
Jiang, ZW .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1999, 33 (03) :531-546
[8]   Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method [J].
Larsson, S ;
Thomee, V ;
Wahlbin, LB .
MATHEMATICS OF COMPUTATION, 1998, 67 (221) :45-71
[9]   Weak Galerkin Finite Element Methods for Parabolic Equations [J].
Li, Qiaoluan H. ;
Wang, Junping .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2013, 29 (06) :2004-2024
[10]   RITZ-VOLTERRA PROJECTIONS TO FINITE-ELEMENT SPACES AND APPLICATIONS TO INTEGRODIFFERENTIAL AND RELATED EQUATIONS [J].
LIN, YP ;
THOMEE, V ;
WAHLBIN, LB .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (04) :1047-1070
1234