Superclose analysis of H¹-Galerkin mixed finite element methods combined with two-grid scheme for semilinear parabolic equations

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.