SUPERCONVERGENCE ANALYSIS FOR TIME-FRACTIONAL DIFFUSION EQUATIONS WITH NONCONFORMING MIXED FINITE ELEMENT METHOD
作者机构：School of Mathematics and Statistics Pingdingshan University Pingdingshan 467000 China School of Mathematics and Statistics Zhengzhou University Zhengzhou 450001 China
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2019年第37卷第4期
页 面：488-505页
核心收录：
学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）]
基 金：the National Natural Science Foundation of China (No. 11671369 11271340).
主 题：Nonconforming MFEM LI method Time-fractional diffusion equations Superconvergence
摘 要：In this paper, a fully discrete scheme based on the LI 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 EQ1^rot element (see Lemma 2.3). Then, by using the proved character of EQ1^rot element, we present the superconvergent estimates for the original variable u in the broken H^1-norm and the flux →p =△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.
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