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Volume 37, Issue 3
An Unfitted $hp$-Interface Penalty Finite Element Method for Elliptic Interface Problems

Haijun Wu & Yuanming Xiao

DOI: 10.4208/jcm.1802-m2017-0219

J. Comp. Math., 37 (2019), pp. 316-339.

Published online: 2018-09

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  • 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).

  • Keywords

Elliptic interface problems, Unfitted mesh, $hp$-IPFEM.

  • AMS Subject Headings

65N12, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hjw@nju.edu.cn (Haijun Wu)

xym@nju.edu.cn (Yuanming Xiao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-316, author = {Wu , Haijun and Xiao , Yuanming}, title = {An Unfitted $hp$-Interface Penalty Finite Element Method for Elliptic Interface Problems}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {3}, pages = {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).

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1802-m2017-0219}, url = {http://global-sci.org/intro/article_detail/jcm/12724.html} }
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 -

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).

Wu , Haijun and Xiao , Yuanming. (2018). An Unfitted $hp$-Interface Penalty Finite Element Method for Elliptic Interface Problems. Journal of Computational Mathematics. 37 (3). 316-339. doi:10.4208/jcm.1802-m2017-0219
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