Long-time behavior of the two-grid finite element method for fully discrete semilinear evolution equations with positive memory

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:250

Article

Wang, Wansheng

关键词: Parabolic integro-differential equations;    Long-time stability;    Error estimates;    Finite element methods;    Space two-grid;    Space-time two-grid;   

DOI  :  10.1016/j.cam.2013.03.006

来源: Elsevier

【 摘 要 】

Based on two-grid discretizations, two fully discrete finite element algorithms for semilinear parabolic integro-differential equations with positive memory are proposed. With the backward Euler scheme for the temporal discretization, the basic idea of the space two-grid finite element algorithms is to approximate the semilinear equations on a coarse space grid and to solve the linearized equations on a finer space grid at each time step. To further decreases the amount of computational work, a space time two-grid algorithm based on a coarse space grid with large time stepsize Delta T and a finer space grid with small time stepsize Delta t for the evolutional equations is proposed in this paper. The sharp long-time stability and error estimates for the standard finite element method, the space two-grid finite element method, and the space time two-grid finite element method are derived. It is showed that the two-grid algorithms' long-time stability and error estimates are similar to those of the direct resolution of the semilinear problem on a fine grid. (C) 2013 Elsevier B.V. All rights reserved.

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