Stability and conditioning of immersed finite element methods: analysis and remedies
Numerical Analysis
2022-08-19 v1 Numerical Analysis
Abstract
This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and the treatment of the adverse effects of small cut elements. We distinguish between adverse effects regarding the stability and adverse effects regarding the conditioning of the system, and we present an overview of the developed remedies. In particular, we provide a detailed explanation of Schwarz preconditioning, element aggregation, and the ghost penalty formulation. Furthermore, we outline the methodologies developed for quadrature and weak enforcement of Dirichlet conditions, and we discuss open questions and future research directions.
Keywords
Cite
@article{arxiv.2208.08538,
title = {Stability and conditioning of immersed finite element methods: analysis and remedies},
author = {Frits de Prenter and Clemens Verhoosel and Harald van Brummelen and Mats Larson and Santiago Badia},
journal= {arXiv preprint arXiv:2208.08538},
year = {2022}
}