The Immersed Finite Volume Element Method for Some Interface Problems with Nonhomogeneous Jump Conditions
Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 3 : pp. 368–382
Abstract
In this paper, an immersed finite volume element (IFVE) method is developed for solving some interface problems with nonhomogeneous jump conditions. Using the source removal technique of nonhomogeneous jump conditions, the new IFVE method is the finite volume element method applied to the equivalent interface problems with homogeneous jump conditions and have properties of the usual finite volume element method. The resulting IFVE scheme is simple and second order accurate with a uniform rectangular partition and the dual meshes. Error analyses show that the new IFVE method with usual $O(h^2)$ convergence in the $L^2$ norm and $O(h)$ in the $H^1$ norm. Numerical examples are also presented to demonstrate the efficiency of the new method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-444
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 3 : pp. 368–382
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Elliptic interface problem non-homogeneous jump conditions immersed finite volume element.