|
TWO-GRID ALGORITHM OF
H
1-GALERKIN MIXED FINITE ELEMENT METHODS FOR SEMILINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS
Tianliang Hou, Chunmei Liu, Chunlei Dai, Luoping Chen, Yin Yang
Journal of Computational Mathematics
2022, 40 (5):
667-685.
DOI: 10.4208/jcm.2101-m2019-0159
In this paper, we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by
H
1-Galerkin mixed finite element methods. We use the lowest order Raviart-Thomas 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 two-grid scheme is presented and its convergence is discussed. In the proposed two-grid 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 two-grid method achieves the same convergence property as the one-grid method with the choice
h =
H
2.
Reference |
Related Articles |
Metrics
|
|