Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations.

Using finite element method in spatial direction and classical L1 approximation in temporal direction, a fully-discrete scheme is established for a class of two-dimensional multi-term time fractional diffusion equations with Caputo fractional derivatives. The stability analysis of the approximate scheme is proposed. The spatial global superconvergence and temporal convergence of order O(h2+2) for the original variable in H1-norm is presented by means of properties of bilinear element and interpolation postprocessing technique, where h and are the step sizes in space and time, respectively. Finally, several numerical examples are implemented to evaluate the efficiency of the theoretical results.