Superconvergence analysis of a new low order nonconforming MFEM for time-fractional diffusion equation

A new low order nonconforming mixed finite element method (MFEM) is proposed and analyzed for time-fractional diffusion equation with element pair (CNRQ1+Q0×Q0). A new error estimate for the consistency error of nonconforming element CNRQ1 is proved, which leads to the superclose and superconvergence results of the original variable in broken H1 norm, and of the flux in L2 norm for a fully-discrete scheme with the Caputo derivative approximated by the classical L1 method. The results obtained herein improve the corresponding conclusions in the previous literature. Finally, some numerical results are provided to confirm the theoretical analysis.