Adv. Appl. Math. Mech., 10 (2018), pp. 752-766.
Published online: 2018-10
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0097}, url = {http://global-sci.org/intro/article_detail/aamm/12234.html} }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.