Highly efficient H1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

doi:10.1007/s10483-014-1833-9

Abstract

Abstract:

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.

Key words: linear triangular element, H¹-Galerkin mixed finite element method (MFEM), asymptotic expansion, superconvergence and extrapolation, parabolic integro-differential equation

2010 MSC Number:

O242.21

Dong-yang SHI;Xin LIAO;Qi-li TANG. Highly efficient H¹-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 897-912.

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Highly efficient H¹-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

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