Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions
Year: 2010
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2009.m9001
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 1 : pp. 23–39
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Immersed interface finite element methods elasticity interface problems singularity removal homogeneous and non-homogeneous jump conditions level-set function.