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

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

2010-07-17

arxiv.org/abs/1007.2893v1

Mathematics

Numerical Analysis

Scientific paper

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.

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