@Article{AAMM-9-2,
author = {Kyeong, Daehyeon and Young, Kwak, Do},
title = {An Immersed Finite Element Method for the Elasticity Problems with Displacement Jump},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {2},
pages = {407--428},
abstract = {<p style="text-align: justify;">In this paper, we propose a finite element method for the elasticity problems
which have displacement discontinuity along the material interface using uniform
grids. We modify the immersed finite element method introduced recently for
the computation of interface problems having homogeneous jumps [20, 22]. Since the
interface is allowed to cut through the element, we modify the standard Crouzeix-Raviart
basis functions so that along the interface, the normal stress is continuous and
the jump of the displacement vector is proportional to the normal stress. We construct
the broken piecewise linear basis functions which are uniquely determined by these
conditions. The unknowns are only associated with the edges of element, except the
intersection points. Thus our scheme has fewer degrees of freedom than most of the
XFEM type of methods in the existing literature [1,8,13]. Finally, we present numerical
results which show optimal orders of convergence rates.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2016.m1427},
url = {https://global-sci.com/article/73258/an-immersed-finite-element-method-for-the-elasticity-problems-with-displacement-jump}
}