TY - JOUR
T1 - A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions
AU - Wang , Liqun
AU - Hou , Songming
AU - Shi , Liwei
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 752
EP - 766
PY - 2018
DA - 2018/10
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2017-0097
UR - https://global-sci.org/intro/article_detail/aamm/12234.html
KW - Finite element method, nonlinear elliptic-parabolic interface problems, nonhomogeneous jump conditions.
AB - <p style="text-align: justify;">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&#39;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.</p>