Two-Grid Immersed Finite Volume Element Methods for Semi-Linear Elliptic Interface Problems with Non-Homogeneous Jump Conditions
Year: 2022
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0339
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 4 : pp. 842–870
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Two-grid immersed finite volume element Cartesian mesh semi-linear non-homogeneous.
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