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Volume 14, Issue 4
Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions

Quanxiang Wang, Liqun Wang & Jianqiang Xie

Adv. Appl. Math. Mech., 14 (2022), pp. 842-870.

Published online: 2022-04

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  • Abstract

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.

  • AMS Subject Headings

65N30

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COPYRIGHT: © Global Science Press

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@Article{AAMM-14-842, author = {}, title = {Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {4}, pages = {842--870}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0339}, url = {http://global-sci.org/intro/article_detail/aamm/20437.html} }
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 -

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.

Quanxiang Wang, Liqun Wang & Jianqiang Xie. (2022). Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions. Advances in Applied Mathematics and Mechanics. 14 (4). 842-870. doi:10.4208/aamm.OA-2020-0339
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