@article{Cao2023, 
author = {Fujun Cao and Dongfang Yuan},
title = {A class of HOC finite difference method for elliptic interface problems with imperfect contact},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {5789-5815},
keywords = {sharp interface, elliptic interface problem, implicit jump conditions, imperfect contact},
url = {https://www.sciopen.com/article/10.3934/math.2023292},
doi = {10.3934/math.2023292},
abstract = {The elliptic interface problems with imperfect contact have found applications in numerical solutions of the Stefan problem of the solidification process and crystal growth, composite materials, multi-phase flows, etc. In this paper a 1D elliptic interface problem with imperfect contact is considered. A class of high-order compact finite difference schemes are constructed on body-fitted and non-body-fitted mesh, respectively. For each case, the second-, third- and fourth-order approximations of implicit jump conditions are provided by using the jump conditions and its high-order derivatives. Numerical examples are provided to verify the performance of the schemes. The numerical results demonstrate that the schemes have theoretical accuracy for elliptic interface problems with imperfect contact.}
}