@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 = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2009.m9001},
url = {http://global-sci.org/intro/article_detail/nmtma/5987.html}
}