An unfitted $hp$-interface penalty finite element method for elliptic interface problems

Haijun Wu; Yuanming Xiao

An unfitted $hp$-interface penalty finite element method for elliptic interface problems

Numerical Analysis 2010-07-20 v1

Authors: Haijun Wu , Yuanming Xiao

Abstract

An $hp$ version of interface penalty finite element method ( $hp$ -IPFEM) is proposed for 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.

Keywords

finite element method finite element methods shape optimization

Cite

@article{arxiv.1007.2893,
  title  = {An unfitted $hp$-interface penalty finite element method for elliptic interface problems},
  author = {Haijun Wu and Yuanming Xiao},
  journal= {arXiv preprint arXiv:1007.2893},
  year   = {2010}
}

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