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Volume 8, Issue 2
Immersed Finite Element Methods for Elliptic Interface Problems with Non-Homogeneous Jump Conditions

X. He, T. Lin & Y. Lin

Int. J. Numer. Anal. Mod., 8 (2011), pp. 284-301.

Published online: 2011-08

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  • Abstract

This paper is to develop immersed finite element (IFE) functions for solving second order elliptic boundary value problems with discontinuous coefficients and non-homogeneous jump conditions. These IFE functions can be formed on meshes independent of interface. Numerical examples demonstrate that these IFE functions have the usual approximation capability expected from polynomials employed. The related IFE methods based on the Galerkin formulation can be considered as natural extensions of those IFE methods in the literature developed for homogeneous jump conditions, and they can optimally solve the interface problems with a nonhomogeneous flux jump condition.

  • Keywords

interface problems, immersed interface, finite element, nonhomogeneous jump conditions.

  • AMS Subject Headings

65N15, 65N30, 65N50, 35R05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-284, author = {X. He, T. Lin and Y. Lin}, title = {Immersed Finite Element Methods for Elliptic Interface Problems with Non-Homogeneous Jump Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {2}, pages = {284--301}, abstract = {

This paper is to develop immersed finite element (IFE) functions for solving second order elliptic boundary value problems with discontinuous coefficients and non-homogeneous jump conditions. These IFE functions can be formed on meshes independent of interface. Numerical examples demonstrate that these IFE functions have the usual approximation capability expected from polynomials employed. The related IFE methods based on the Galerkin formulation can be considered as natural extensions of those IFE methods in the literature developed for homogeneous jump conditions, and they can optimally solve the interface problems with a nonhomogeneous flux jump condition.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/686.html} }
TY - JOUR T1 - Immersed Finite Element Methods for Elliptic Interface Problems with Non-Homogeneous Jump Conditions AU - X. He, T. Lin & Y. Lin JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 284 EP - 301 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/686.html KW - interface problems, immersed interface, finite element, nonhomogeneous jump conditions. AB -

This paper is to develop immersed finite element (IFE) functions for solving second order elliptic boundary value problems with discontinuous coefficients and non-homogeneous jump conditions. These IFE functions can be formed on meshes independent of interface. Numerical examples demonstrate that these IFE functions have the usual approximation capability expected from polynomials employed. The related IFE methods based on the Galerkin formulation can be considered as natural extensions of those IFE methods in the literature developed for homogeneous jump conditions, and they can optimally solve the interface problems with a nonhomogeneous flux jump condition.

X. He, T. Lin and Y. Lin. (2011). Immersed Finite Element Methods for Elliptic Interface Problems with Non-Homogeneous Jump Conditions. International Journal of Numerical Analysis and Modeling. 8 (2). 284-301. doi:
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