Abstract
In this paper, two classes of finite element methods (FEMs) for the two-dimensional time fractional diffusion equation (TFDE) with non-smooth solution are proposed and analyzed. In the temporal direction, we adopt nonuniform L2-1σ method, and in the spatial direction, the conforming bilinear element and the nonconforming modified quasi-Wilson element are utilized. For the proposed conforming and nonconforming FEMs, by using new fractional discrete Grönwall inequalities, the theoretical analysis including the L2-norm error estimates and H1-norm superclose results are given in details. Furthermore, by virtue of the interpolated postprocessing techniques, the global H1-norm superconvergence results are presented. Finally, some numerical results illustrate the correctness of theoretical analysis.
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