High accuracy analysis of an H1-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations

In this paper, an H1-Galerkin mixed finite element approximate scheme is established for a class of two-dimensional time fractional diffusion equations by using the bilinear element, Raviart-Thomas element and L1 time stepping method, which is unconditionally stable and free of LBB condition. And then, without the classical Ritz projection, superclose results for the original variable u in H1-norm and the flux p→=∇u in H(div,Ω)-norm are derived by means of properties of the elements and L1 approximation. Furthermore, with the help of the interpolation postprocessing operator, the global superconvergence results for the original variable u in H1-norm are obtained. Finally, numerical simulations verify that the theoretical results are true on both regular meshes and anisotropic meshes.