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.
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页码：897 / 912
页数：16
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