A locally modified second-order finite element method for interface problems and its implementation in 2 dimensions
Abstract
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is based on a fixed structured coarse mesh, which is then refined into sub-elements to resolve an interior interface. In this work, we extend the locally modified finite element method {in two space dimensions} to second order using an isoparametric approach in the interface elements. Thereby we need to take care that the resulting curved edges do not lead to degenerate sub-elements. We prove optimal a priori error estimates in the -norm and in a discrete energy norm. Finally, we present numerical examples to substantiate the theoretical findings.
Cite
@article{arxiv.2007.13906,
title = {A locally modified second-order finite element method for interface problems and its implementation in 2 dimensions},
author = {Stefan Frei and Gozel Judakova and Thomas Richter},
journal= {arXiv preprint arXiv:2007.13906},
year = {2023}
}