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Volume 3, Issue 1
Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

Yan Gong & Zhilin Li

DOI: 10.4208/nmtma.2009.m9001

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 23-39.

Published online: 2010-03

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  • Abstract

In this paper, a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions. Simple non-body-fitted meshes are used. For homogeneous jump conditions, both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions, a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface. With such a pair of functions, the discontinuities across the interface in the solution and flux are removed; and an equivalent elasticity interface problem with homogeneous jump conditions is formulated. Numerical examples are presented to demonstrate that such methods have second order convergence.

  • Keywords

Immersed interface finite element methods, elasticity interface problems, singularity removal, homogeneous and non-homogeneous jump conditions, level-set function.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-23, author = {Yan Gong and Zhilin Li}, title = {Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {1}, pages = {23--39}, abstract = {

In this paper, a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions. Simple non-body-fitted meshes are used. For homogeneous jump conditions, both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions, a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface. With such a pair of functions, the discontinuities across the interface in the solution and flux are removed; and an equivalent elasticity interface problem with homogeneous jump conditions is formulated. Numerical examples are presented to demonstrate that such methods have second order convergence.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m9001}, url = {http://global-sci.org/intro/article_detail/nmtma/5987.html} }
TY - JOUR T1 - Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions AU - Yan Gong & Zhilin Li JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 23 EP - 39 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2009.m9001 UR - https://global-sci.org/intro/article_detail/nmtma/5987.html KW - Immersed interface finite element methods, elasticity interface problems, singularity removal, homogeneous and non-homogeneous jump conditions, level-set function. AB -

In this paper, a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions. Simple non-body-fitted meshes are used. For homogeneous jump conditions, both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions, a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface. With such a pair of functions, the discontinuities across the interface in the solution and flux are removed; and an equivalent elasticity interface problem with homogeneous jump conditions is formulated. Numerical examples are presented to demonstrate that such methods have second order convergence.

Yan Gong and Zhilin Li. (2010). Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions. Numerical Mathematics: Theory, Methods and Applications. 3 (1). 23-39. doi:10.4208/nmtma.2009.m9001
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