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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 5/2022

29-11-2021 | Original Research

A two-gird method for finite element solution of parabolic integro-differential equations

Author: Keyan Wang

Published in: Journal of Applied Mathematics and Computing | Issue 5/2022

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Abstract

In this paper, we study the unconditional convergence and error estimates of a two-grid finite element method for the semilinear parabolic integro-differential equations. By using a temporal-spatial error splitting technique, optimal \(L^p\) and \(H^1\) error estimates of the finite element method can be obtained. Moreover, to deal with the semilinearity of the model, we use the two-grid method. Optimal error estimates in \(L^2\) and \(H^1\)-norms of two-grid solution are derived without any time-step size conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.
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Metadata
Title
A two-gird method for finite element solution of parabolic integro-differential equations
Author
Keyan Wang
Publication date
29-11-2021
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 5/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-021-01670-2

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