TY - JOUR
T1 - An Unfitted $hp$-Interface Penalty Finite Element Method for Elliptic Interface Problems
AU - Wu , Haijun
AU - Xiao , Yuanming
JO - Journal of Computational Mathematics
VL - 3
SP - 316
EP - 339
PY - 2018
DA - 2018/09
SN - 37
DO - http://doi.org/10.4208/jcm.1802-m2017-0219
UR - https://global-sci.org/intro/article_detail/jcm/12724.html
KW - Elliptic interface problems, Unfitted mesh, $hp$-IPFEM.
AB - <p style="text-align: justify;">An $hp$ version of interface penalty finite element method ($hp$-IPFEM) is proposed to
solve the elliptic interface problems in two and three dimensions on unfitted meshes. Error
estimates in broken $H^1$ norm, which are optimal with respect to $h$ and suboptimal with
respect to $p$ by half an order of $p$, are derived. Both symmetric and non-symmetric IPFEM
are considered. Error estimates in $L^2$ norm are proved by the duality argument. All the
estimates are independent of the location of the interface relative to the meshes. Numerical
examples are provided to illustrate the performance of the method. This paper is adapted
from the work originally post on arXiv.com by the same authors (arXiv:1007.2893v1).</p>