Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations

By means of spatial quasi-Wilson nonconforming finite element and classical L1 approximation, an unconditionally stable fully-discrete scheme for two-dimensional time fractional diffusion equations is established. Moreover, convergence results in L-2-norm and broken H-1-norm and the corresponding superclose and superconvergence results in spatial direction in broken H-1-norm are obtained by use of special properties of quasi-Wilson element. At the same time, the optimal order error estimate in temporal direction is derived by dealing with fractional derivative skillfully. Finally, numerical results demonstrate that the approximate scheme provides valid and efficient way for solving the time-fractional diffusion equation. Crown Copyright (C) 2016 Published by Elsevier Ltd. All rights reserved.