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

作     者：石东洋 廖歆 唐启立 Dong-yang SHI;Xin LIAO;Qi-li TANG

作者机构：School of Mathematics and Statistics Zhengzhou University 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2014年第35卷第7期

页      面：897-912页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10971203,11271340,and 11101381) the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006) 

主　　题：parabolic integro-differential equation H1-Galerkin mixed finite elementmethod (MFEM) linear triangular element asymptotic expansion superconvergence andextrapolation 

摘      要：A highly efficient H1-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 H1 （Ω） norm and the flux p = u in H（div, Ω） 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.