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 

机构地区：[1]School of Mathematics and Statistics, Zhengzhou University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第7期897-912,共16页应用数学和力学（英文版）

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)

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.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.

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

分 类 号：O241.82[理学—计算数学]