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A Numerical Method for Solving Two-Dimensional Elliptic Interface Problems with Nonhomogeneous Flux Jump Condition and Nonlinear Jump Condition

  • Liqun Wang , Songming Hou and Liwei Shi EMAIL logo
Published/Copyright: May 9, 2017

Abstract

In this paper, we propose a new method for solving two-dimensional elliptic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition. The method we used is traditional finite element method coupled with Newton’s method, it is very simple and easy to implement. The grid we used here is body-fitting grids based on the idea of semi-Cartesian grid. Numerical experiments show that this method is about second order accurate in the L norm.

MSC 2010: 65N30

Funding statement: L. Shi’s research is supported by Science Foundations of China University of Political Science and Law (Nos. 1000-10816106 and 1000-10816330). S. Hou’s research is supported by NSF grant DMS-1317994 and Dr. Walter Koss Professorship. L. Wang’s research is supported by Science Foundations of China University of Petroleum-Beijing (Nos. 2462015BJB05, 2462015YQ0604 and 2462015QZDX02).

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Received: 2016-7-22
Accepted: 2017-3-28
Published Online: 2017-5-9
Published in Print: 2017-5-24

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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