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Volume 13, Issue 3
The Immersed Finite Volume Element Method for Some Interface Problems with Nonhomogeneous Jump Conditions

L. Zhu, Z.-Y. Zhang & Z.-L. Li

Int. J. Numer. Anal. Mod., 13 (2016), pp. 368-382.

Published online: 2016-05

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  • 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.

  • Keywords

Elliptic interface problem, non-homogeneous jump conditions, immersed finite volume element.

  • AMS Subject Headings

65N08, 65N50, 35R05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-368, author = {L. Zhu, Z.-Y. Zhang and Z.-L. Li}, title = {The Immersed Finite Volume Element Method for Some Interface Problems with Nonhomogeneous Jump Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/444.html} }
TY - JOUR T1 - The Immersed Finite Volume Element Method for Some Interface Problems with Nonhomogeneous Jump Conditions AU - L. Zhu, Z.-Y. Zhang & Z.-L. Li JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 368 EP - 382 PY - 2016 DA - 2016/05 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/444.html KW - Elliptic interface problem, non-homogeneous jump conditions, immersed finite volume element. AB -

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.

L. Zhu, Z.-Y. Zhang and Z.-L. Li. (2016). The Immersed Finite Volume Element Method for Some Interface Problems with Nonhomogeneous Jump Conditions. International Journal of Numerical Analysis and Modeling. 13 (3). 368-382. doi:
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