A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions

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.