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

Yaxin Hou; Cao Wen; Yang Liu; Hong Li; Yaxin Hou; Cao Wen; Yang Liu; Hong Li

doi:10.3934/nhm.2023037

Networks and Heterogeneous Media

2023, Volume 18, Issue 2: 855-876. doi: 10.3934/nhm.2023037

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

Yaxin Hou ^1,†,
Cao Wen ^2,†,
Yang Liu ^{2
,
,},
Hong Li ^{2
,
,}

1.
Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China
2.
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
† These authors contributed equally to this work

Received: 24 December 2022 Revised: 21 February 2023 Accepted: 22 February 2023 Published: 13 March 2023

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.
- nonlinear distributed-order fractional sub-diffusion equation,
- WSGD operator,
- two-grid ADI FE method,
- stability,
- error estimates
Citation: Yaxin Hou, Cao Wen, Yang Liu, Hong Li. A two-grid ADI finite element approximation for a nonlinear distributed-order fractional sub-diffusion equation[J]. Networks and Heterogeneous Media, 2023, 18(2): 855-876. doi: 10.3934/nhm.2023037

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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.

References

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