Highly efficient H 1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

被引：8

作者：

Shi, Dong-yang ^{[1
]}

Liao, Xin ^{[1
]}

Tang, Qi-li ^{[1
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

来源：

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION | 2014年 / 35卷 / 07期

基金：

中国国家自然科学基金;

关键词：

parabolic integro-differential equation; H-1-Galerkin mixed finite element method (MFEM); linear triangular element; asymptotic expansion; superconvergence and extrapolation; APPROXIMATIONS;

D O I：

10.1007/s10483-014-1833-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A highly efficient H (1)-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h (2)) for both the original variable u in H (1)(Omega) norm and the flux p = a double dagger u in H (div,Omega) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h (3)) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.

引用

页码：897 / 912

页数：16

共 25 条

[1] Apel T, 2001, NUMER MATH, V89, P193, DOI 10.1007/s002110000256
[2] FINITE-ELEMENT APPROXIMATION OF A PARABOLIC INTEGRODIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL
CHEN, C
THOMEE, V
WAHLBIN, LB
[J]. MATHEMATICS OF COMPUTATION, 1992, 58 (198) : 587 - 602
[3] [陈红斌 CHEN HONGBIN], 2008, [应用数学学报, Acta Mathematicae Applicatae Sinica], V31, P702
[4] Ewing R, 2000, NUMER METH PART D E, V16, P285, DOI 10.1002/(SICI)1098-2426(200005)16:3<285::AID-NUM2>3.0.CO
[5] 2-3
[6] SPLINE COLLOCATION METHODS FOR A CLASS OF HYPERBOLIC PARTIAL INTEGRODIFFERENTIAL EQUATIONS
FAIRWEATHER, G
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (02) : 444 - 460
[7] Least-squares Galerkin procedures for parabolic integro-differential equations
Guo, H
Rui, HX
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 150 (03) : 749 - 762
[8] Two splitting positive definite mixed finite element methods for parabolic integro-differential equations
Guo, Hui
Zhang, Jiansong
Fu, Hongfei
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (22) : 11255 - 11268
[9] H1-Galerkin mixed finite element method for the regularized long wave equation
Guo, L
Chen, H
[J]. COMPUTING, 2006, 77 (02) : 205 - 221
[10] Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media
Jia, Shanghui
Li, Deli
Liu, Tang
Zhang, Shuhua
[J]. APPLICATIONS OF MATHEMATICS, 2008, 53 (01) : 13 - 39

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