TY - JOUR
T1 - Optimal Quadratic Nitsche Extended Finite Element Method for Interface Problem of Diffusion Equation
AU - Wang , Fei
AU - Zhang , Shuo
JO - Journal of Computational Mathematics
VL - 5
SP - 693
EP - 717
PY - 2018
DA - 2018/06
SN - 36
DO - http://doi.org/10.4208/jcm.1703-m2015-0340
UR - https://global-sci.org/intro/article_detail/jcm/12453.html
KW - Interface problems, Extended finite element methods, Error estimates, Nitsche's scheme, Quadratic element.
AB - <p style="text-align: justify;">In this paper, we study Nitsche extended finite element method (XFEM) for the interface
problem of a two dimensional diffusion equation. Specifically, we study the quadratic
XFEM scheme on some shape-regular family of grids and prove the optimal convergence
rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying
the cases of intersection between the elements and the interface and prove a weighted trace
inequality for the extended finite element functions needed, and the general framework of
analysing XFEM can be implemented then.</p>