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Volume 42, Issue 5
A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact

Fujun Cao, Dongfang Yuan, Dongxu Jia & Guangwei Yuan

DOI: 10.4208/jcm.2302-m2022-0111

J. Comp. Math., 42 (2024), pp. 1328-1355.

Published online: 2024-07

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  • 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.

  • Keywords

Finite difference method, Elliptic interface problem, Imperfect contact.

  • AMS Subject Headings

65N06, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-42-1328, author = {Cao , FujunYuan , DongfangJia , Dongxu and Yuan , Guangwei}, title = {A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2302-m2022-0111}, url = {http://global-sci.org/intro/article_detail/jcm/23280.html} }
TY - JOUR T1 - A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact AU - Cao , Fujun AU - Yuan , Dongfang AU - Jia , Dongxu AU - Yuan , Guangwei JO - Journal of Computational Mathematics VL - 5 SP - 1328 EP - 1355 PY - 2024 DA - 2024/07 SN - 42 DO - http://doi.org/10.4208/jcm.2302-m2022-0111 UR - https://global-sci.org/intro/article_detail/jcm/23280.html KW - Finite difference method, Elliptic interface problem, Imperfect contact. AB -

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.

Cao , FujunYuan , DongfangJia , Dongxu and Yuan , Guangwei. (2024). A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact. Journal of Computational Mathematics. 42 (5). 1328-1355. doi:10.4208/jcm.2302-m2022-0111
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