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 - <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>