Volume 10, Issue 3
A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions

Liqun Wang, Songming Hou & Liwei Shi

Adv. Appl. Math. Mech., 10 (2018), pp. 752-766.

Published online: 2018-10

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  • 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 elementmethod coupledwith 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.

  • Keywords

Finite element method, nonlinear elliptic-parabolic interface problems, nonhomogeneous jump conditions.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-752, author = {}, title = {A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {3}, pages = {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 elementmethod coupledwith 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} }
TY - JOUR T1 - A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 752 EP - 766 PY - 2018 DA - 2018/10 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0097 UR - https://global-sci.org/intro/aamm/12234.html KW - Finite element method, nonlinear elliptic-parabolic interface problems, nonhomogeneous jump conditions. AB - 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 elementmethod coupledwith 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.
Liqun Wang, Songming Hou & Liwei Shi. (2020). A FEM for Solving Two-Dimensional Nonlinear Elliptic-Parabolic Interface Problems with Nonhomogeneous Jump Conditions. Advances in Applied Mathematics and Mechanics. 10 (3). 752-766. doi:10.4208/aamm.OA-2017-0097
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