Open Access

ARTICLE

A Simple FEM for Solving Two-Dimensional Diffusion Equation with Nonlinear Interface Jump Conditions

Liqun Wang¹, Songming Hou², Liwei Shi^3,∗

1 China University of Petroleum-Beijing, Deptartment of Mathematics, College of Science, Beijing, 102249, China.
2 Louisiana Tech University, Deptartment of Mathematics and Statistics, LA, Rustion, 71272, USA.
3 China University of Political Science and Law, Deptartment of Science and Technology, Beijing, 102249, China.

* Corresponding Author: Liwei Shi. Email: .

(This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)

Computer Modeling in Engineering & Sciences 2019, 119(1), 73-90. https://doi.org/10.32604/cmes.2019.04581

Abstract

In this paper, we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition. The main idea is to use traditional finite element method on semi-Cartesian mesh coupled with Newton’s method to handle nonlinearity. It is easy to implement even though variable coefficients are used in the jump condition instead of constant in previous work for elliptic interface problem. Numerical experiments show that our method is about second order accurate in the L^∞ norm.

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Keywords

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