TY - JOUR
T1 - A Nonconforming Nitsche's Extended Finite Element Method for Elliptic Interface Problems
AU - Wang , Nan
AU - Chen , Jinru
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 879
EP - 901
PY - 2020
DA - 2020/06
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2018-0252
UR - https://global-sci.org/intro/article_detail/aamm/16931.html
KW - Nonconforming extended finite element, Nitsche's method, elliptic interface problems, interface-unfitted mesh.
AB - <p style="text-align: justify;">This article proposes a new $P_{1}$ nonconforming Nitsche&#39;s extended finite element method for elliptic interface problems with interface-unfitted meshes. It is shown that the stability of the discrete formulation is independent of not only the mesh size and the diffusion parameters, but also the position of the interface, showing a robustness over the location of interface. In spite of the low regularity of interface problems, the optimal convergence is obtained. Numerical experiments are carried out to validate theoretical results.</p>