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

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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