Applied Mathematics and Mechanics >
Highly efficient H1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation
Received date: 2013-07-14
Revised date: 2013-09-21
Online published: 2014-07-01
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 10971203, 11271340, and 11101381) and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20094101110006)
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(h2) 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(h3) 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.
Dong-yang SHI;Xin LIAO;Qi-li TANG . Highly efficient H1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation[J]. Applied Mathematics and Mechanics, 2014 , 35(7) : 897 -912 . DOI: 10.1007/s10483-014-1833-9
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