Abstract
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.
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