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An Unfitted $hp$-Interface Penalty Finite Element Method for Elliptic Interface Problems

An Unfitted $hp$-Interface Penalty Finite Element Method for Elliptic Interface Problems
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Year:    2019

Author:    Haijun Wu, Yuanming Xiao

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 3 : pp. 316–339

Abstract

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).

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1802-m2017-0219

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 3 : pp. 316–339

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Elliptic interface problems Unfitted mesh $hp$-IPFEM.

Author Details

Haijun Wu

Yuanming Xiao

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