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.