SUPERCONVERGENCE ANALYSIS FOR TIME-FRACTIONAL DIFFUSION EQUATIONS WITH NONCONFORMING MIXED FINITE ELEMENT METHOD

In this paper, a fully discrete scheme based on the L1 approximation in temporal direction for the fractional derivative of order in (0, 1) and nonconforming mixed finite element method (MFEM) in spatial direction is established. First, we prove a novel result of the consistency error estimate with order O(h(2)) of EQ(1)(rot) element (see Lemma 2.3). Then, by using the proved character of EQ(1rot) element, we present the superconvergent estimates for the original variable u in the broken H-1-norm and the flux (p) over right arrow = del u in the (L-2)(2)-norm under a weaker regularity of the exact solution. Finally, numerical results are provided to confirm the theoretical analysis.