
TWOGRID ALGORITHM OF
H
^{1}GALERKIN MIXED FINITE ELEMENT METHODS FOR SEMILINEAR PARABOLIC INTEGRODIFFERENTIAL EQUATIONS
Tianliang Hou, Chunmei Liu, Chunlei Dai, Luoping Chen, Yin Yang
Journal of Computational Mathematics
2022, 40 (5):
667685.
DOI: 10.4208/jcm.2101m20190159
In this paper, we present a twogrid discretization scheme for semilinear parabolic integrodifferential equations by
H
^{1}Galerkin mixed finite element methods. We use the lowest order RaviartThomas mixed finite elements and continuous linear finite element for spatial discretization, and backward Euler scheme for temporal discretization. Firstly, a priori error estimates and some superclose properties are derived. Secondly, a twogrid scheme is presented and its convergence is discussed. In the proposed twogrid scheme, the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal accuracy. Finally, a numerical experiment is implemented to verify theoretical results of the proposed scheme. The theoretical and numerical results show that the twogrid method achieves the same convergence property as the onegrid method with the choice
h =
H
^{2}.
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