A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact

A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact

Year:    2024

Author:    Fujun Cao, Dongfang Yuan, Dongxu Jia, Guangwei Yuan

Journal of Computational Mathematics, Vol. 42 (2024), Iss. 5 : pp. 1328–1355

Abstract

In this paper two dimensional elliptic interface problem with imperfect contact is considered, which is featured by the implicit jump condition imposed on the imperfect contact interface, and the jumping quantity of the unknown is related to the flux across the interface. A finite difference method is constructed for the 2D elliptic interface problems with straight and curve interface shapes. Then, the stability and convergence analysis are given for the constructed scheme. Further, in particular case, it is proved to be monotone. Numerical examples for elliptic interface problems with straight and curve interface shapes are tested to verify the performance of the scheme. The numerical results demonstrate that it obtains approximately second-order accuracy for elliptic interface equations with implicit jump condition.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2302-m2022-0111

Journal of Computational Mathematics, Vol. 42 (2024), Iss. 5 : pp. 1328–1355

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Finite difference method Elliptic interface problem Imperfect contact.

Author Details

Fujun Cao

Dongfang Yuan

Dongxu Jia

Guangwei Yuan