TY - JOUR
T1 - Superconvergence Analysis for Time-Fractional Diffusion Equations with Nonconforming Mixed Finite Element Method
AU - Zhang , Houchao
AU - Shi , Dongyang
JO - Journal of Computational Mathematics
VL - 4
SP - 488
EP - 505
PY - 2019
DA - 2019/02
SN - 37
DO - http://doi.org/10.4208/jcm.1805-m2017-0256
UR - https://global-sci.org/intro/article_detail/jcm/13005.html
KW - Nonconforming MFEM, $L1$ method, Time-fractional diffusion equations, Superconvergence.
AB - <p style="text-align: justify;">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 $EQ^{rot}_1$ element (see Lemma 2.3).
Then, by using the proved character of $EQ^{rot}_1$ element, we present the superconvergent
estimates 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 are
provided to confirm the theoretical analysis.</p>