#### Liping Zhou, Meina Wei, Superclose analysis of \$H^1\$-Galerkin mixed finite element methods combined with two-grid scheme for semilinear parabolic equations, Vol. 2023 (2023), Article ID 3, pp. 1-13

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DOI: 10.23952/jnfa.2023.3

Received October 14, 2022; Accepted December 2, 2022; Published January 28, 2023

Abstract In this paper, we investigate a two-grid scheme for semilinear parabolic equations discretized by $H^1$-Galerkin mixed finite element method combined with Crank-Nicolson scheme. Based on the interpolation and duality argument technique, we discuss superclose properties for two-grid method and $H^1$-Galerkin mixed finite element method. The interpolation theory plays an important role in convergence analysis. Theoretical results demonstrate that the two methods have the same convergence order by choosing $h=H^2$. Finally, a numerical example is given to verify the theoretical results.

L. Zhou, M. Wei, Superclose analysis of $H^1$-Galerkin mixed finite element methods combined with two-grid scheme for semilinear parabolic equations, J. Nonlinear Funct. Anal. 2023 (2023) 3.