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 - <p style="text-align: justify;">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.</p>