An Unfitted $hp$-Interface Penalty Finite Element Method for Elliptic Interface Problems (Journal of Computational Mathematics, 2019)
An $hp$ version of interface penalty finite element method ($hp$-IPFEM) is proposed tosolve the elliptic interface problems in two and three dimensions on unfitted meshes. Errorestimates in broken $H^1$ norm, which are optimal with respect to $h$ and suboptimal withrespect to $p$ by half an order of $p$, are derived. Both symmetric and non-symmetric IPFEMare considered. Error estimates in $L^2$ norm are proved by the duality argument. All theestimates are independent of the location of the interface relative to the meshes. Numericalexamples are provided to illustrate the performance of the method. This paper is adaptedfrom the work originally post on arXiv.com by the same authors (arXiv:1007.2893v1).