A class of HOC finite difference method for elliptic interface problems with imperfect contact

Fujun Cao; Dongfang Yuan; Fujun Cao; Dongfang Yuan

doi:10.3934/math.2023292

AIMS Mathematics

2023, Volume 8, Issue 3: 5789-5815. doi: 10.3934/math.2023292

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A class of HOC finite difference method for elliptic interface problems with imperfect contact

Fujun Cao ^{1,2
,
,},
Dongfang Yuan ^1,2

1.
School of Science, Inner Mongolia University of Science and Technology, Baotou, China
2.
School of Mathematics and Science, Inner Mongolia Normal University, Hohhot, China

Received: 10 October 2022 Revised: 15 November 2022 Accepted: 28 November 2022 Published: 26 December 2022
MSC : 35J40, 35R05

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.
- implicit jump conditions,
- elliptic interface problem,
- imperfect contact,
- sharp interface
Citation: Fujun Cao, Dongfang Yuan. A class of HOC finite difference method for elliptic interface problems with imperfect contact[J]. AIMS Mathematics, 2023, 8(3): 5789-5815. doi: 10.3934/math.2023292

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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.

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