A new approach of superconvergence analysis for two-dimensional time fractional diffusion equation

被引：11

作者：

Shi, Dongyang ^{[1
]}

Yang, Huaijun ^{[1
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 75卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Time-fractional diffusion equation; Bilinear finite element; Fully-discrete scheme; Superclose and superconvergence; NONCONFORMING FINITE-ELEMENT; SUBDIFFUSION EQUATION; NUMERICAL-SOLUTION; CONVERGENCE;

D O I：

10.1016/j.camwa.2018.01.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new approach of superconvergent estimate of bilinear finite element is established for two-dimensional time-fractional diffusion equation under fully-discrete scheme. The novelty of this approach is the combination technique of the interpolation and Ritz projection as well as the superclose estimate in H-1-norm between them, which avoids the difficulty of constructing a postprocessing operator for Ritz projection operator, and reduces the regularity requirement of the exact solution. At the same time, three numerical examples are carried out to verify the theoretical analysis. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：3012 / 3023

页数：12

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