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arXiv · 1007.2893

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

Haijun Wu·Yuanming Xiao
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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.

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Haijun Wu, Yuanming Xiao. 2010-07-17. An unfitted $hp$-interface penalty finite element method for elliptic interface problems. https://arxiv.org/abs/1007.2893

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