Superconvergence Analysis for Time-Fractional Diffusion Equations with Nonconforming Mixed Finite Element Method (Journal of Computational Mathematics, 2019)
In this paper, a fully discrete scheme based on the $L1$ approximation in temporaldirection for the fractional derivative of order in (0, 1) and nonconforming mixed finiteelement method (MFEM) in spatial direction is established. First, we prove a novel resultof the consistency error estimate with order $O(h^2)$ of $EQ^{rot}_1$ element (see Lemma 2.3).Then, by using the proved character of $EQ^{rot}_1$ element, we present the superconvergentestimates for the original variable $u$ in the broken $H^1$-norm and the flux $\vec{q} = ∇u$ in the $(L^2)^2$-norm under a weaker regularity of the exact solution. Finally, numerical results areprovided to confirm the theoretical analysis.