@Article{JCM-37-4,
author = {Zhang, Houchao and Shi, Dongyang},
title = {Superconvergence Analysis for Time-Fractional Diffusion Equations with Nonconforming Mixed Finite Element Method},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {4},
pages = {488--505},
abstract = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1805-m2017-0256},
url = {https://global-sci.com/article/84423/superconvergence-analysis-for-time-fractional-diffusion-equations-with-nonconforming-mixed-finite-element-method}
}