Volume 57, Number 3, May-June 2023
|Page(s)||1355 - 1380|
|Published online||12 May 2023|
A locally modified second-order finite element method for interface problems and its implementation in 2 dimensions
Department of Mathematics & Statistics, University of Konstanz, Konstanz, Germany
2 Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany
* Corresponding author: email@example.com
The locally modified finite element method, which is introduced in Frei and Richter [SIAM J. Numer. Anal. 52 (2014) 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 L2-norm and in a discrete energy norm. Finally, we present numerical examples to substantiate the theoretical findings.
Mathematics Subject Classification: 65N30 / 65N15
Key words: Fitted finite elements / interface problem / a priori error estimates / weak discontinuities
© The authors. Published by EDP Sciences, SMAI 2023
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