A class of HOC finite difference method for elliptic interface problems with imperfect contact-Reference-Cited by-同舟云学术

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

Published:2022 Issue:3 Volume:8 Page:5789-5815
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Cao Fujun¹²,Yuan Dongfang¹²

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference47 articles.

1. A. A. Samarskii, V. B. Andreev, Differential method for elliptic equations [in Russian], Nauka, Moscow, 1976.

2. A. A. Samarskii, The theroy of difference scheme, Marcel Dekker, Inc., 2001.

3. A. A. Samarskii, P. N. Vabishchevich, Computational heat transfer, Vol. 1, John Wiley & Sons Ltd, 1995.

4. Z. Q. Huang, E. J. Ding, Transport theory, 2 Eds., Beijing: Science Press, 2008.

5. G. Lopez-Ruiz, J. Bravo-Castillero, R. Brenner, M. E. Cruzd, R. Guinovart-Díazb, L. D. Pérez-Fernándeze, et al., Variational bounds in composites with nonuniform interfacial thermal resistance, Appl. Math. Model., 39 (2015), 7266–7276. https://doi.org/10.1016/j.apm.2015.02.048