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Research Article | Open Access

A two-grid ADI finite element approximation for a nonlinear distributed-order fractional sub-diffusion equation

Yaxin Hou1,†, Cao Wen2,†, Yang Liu2( ), Hong Li2( )
Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

† These authors contributed equally to this work

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Abstract

In this paper, a two-grid alternating direction implicit (ADI) finite element (FE) method based on the weighted and shifted Grünwald difference (WSGD) operator is proposed for solving a two-dimensional nonlinear time distributed-order fractional sub-diffusion equation. The stability and optimal error estimates with second-order convergence rate in spatial direction are obtained. The storage space can be reduced and computing efficiency can be improved in this method. Two numerical examples are provided to verify the theoretical results.

Keywords

nonlinear distributed-order fractional sub-diffusion equationWSGD operatortwo-grid ADI FE methodstabilityerror estimates

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Networks and Heterogeneous Media
Volume 18 Issue 2,
June 2023
Pages 855-876
DOI: 10.3934/nhm.2023037

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Cite this article:
Hou Y, Wen C, Liu Y, et al. A two-grid ADI finite element approximation for a nonlinear distributed-order fractional sub-diffusion equation. Networks and Heterogeneous Media, 2023, 18(2): 855-876. https://doi.org/10.3934/nhm.2023037

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Received: 24 December 2022
Revised: 21 February 2023
Accepted: 22 February 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)