TY - JOUR
T1 - Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 842
EP - 870
PY - 2022
DA - 2022/04
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2020-0339
UR - https://global-sci.org/intro/article_detail/aamm/20437.html
KW - Two-grid, immersed finite volume element, Cartesian mesh, semi-linear, non-homogeneous.
AB - <p style="text-align: justify;">In this paper, we propose an immersed finite volume element method for solving the semi-linear elliptic interface problems with non-homogeneous jump conditions. Furthermore, two-grid techniques are used to improve the computational efficiency. In this way, we only need to solve a non-linear system on the coarse grid, and a linear system on the fine grid. Numerical results illustrate that the proposed method can solve the semi-linear elliptic interface problems efficiently. Approximate second-order accuracy for the solution in the $L^{\infty}$ norm can be obtained for the considered examples.</p>