@Article{JCM-40-667,
author = {Hou , TianliangLiu , ChunmeiDai , ChunleiChen , Luoping and Yang , Yin},
title = {Two-Grid Algorithm of $H^{1}$-Galerkin Mixed Finite Element Methods for Semilinear Parabolic Integro-Differential Equations},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {40},
number = {5},
pages = {667--685},
abstract = {<p style="text-align: justify;">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 $h=H^2$.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2101-m2019-0159},
url = {http://global-sci.org/intro/article_detail/jcm/20542.html}
}