A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions
Year: 2018
Author: Liqun Wang, Songming Hou, Liwei Shi
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 3 : pp. 752–766
Abstract
In this paper, a new method was proposed for solving two-dimensional nonlinear elliptic-parabolic interface problems with nonhomogeneous jump conditions. The method we used is a 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 for different kinds of nonlinear terms and interface with complicated geometry.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2017-0097
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 3 : pp. 752–766
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Finite element method nonlinear elliptic-parabolic interface problems nonhomogeneous jump conditions.