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

Abstract

AbstractIn 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 $L^\infty$ norm.