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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

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 = {}, 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 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 & Zhilin Li. (2020). 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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