Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 86, Issue -, Pages 1-15Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2020.12.016
Keywords
Bilinear; Interface problems; Cartesian mesh; Finite volume element; Non-homogeneous
Categories
Funding
- National Natural Science Foundation of China [11701283, 11971241]
- Fundamental Research Funds for the Central Universities, China [KJQN201839]
- Excellent Young Talents Science and Technology Fund of College of Engineering, China [YQ 201607]
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This paper presents a new bilinear immersed finite volume element method based on rectangular mesh to solve elliptic interface problems with non-homogeneous jump conditions and sharp-edged interfaces. Numerical experiments show that the method achieves nearly second-order accuracy for the solution and first-order accuracy for the solution gradient in the L-infinity norm.
In this paper, a new bilinear immersed finite volume element method based on rectangular mesh is presented to solve the elliptic interface problems with non-homogeneous jump conditions and sharp-edged interfaces. This method is capable of dealing with the case when the interface passes through grid points and when the solutions are oscillating. Plenty of numerical experiments show that our method is nearly second-order accuracy for the solution and is first-order accuracy for the gradient of the solution in the L-infinity norm. (C) 2021 Elsevier Ltd. All rights reserved.
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