Stability and conditioning of immersed finite element methods

analysis and remedies

Review (2023)

Authors

Frits de Prenter Wind Energy - Aerospace Engineering
Clemens Verhoosel Eindhoven University of Technology
Harald van Brummelen Eindhoven University of Technology
Mats Larson Umeå University
Santiago Badia Monash University
Research Group
Wind Energy (Aerospace Engineering) (TU Delft)
Copyright: © 2023 Frits de Prenter, Clemens Verhoosel, Harald van Brummelen, Mats Larson, Santiago Badia
DOI: https://doi.org/10.1007/s11831-023-09913-0
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Published Date

2023

Language

English

Faculty

Aerospace Engineering

Department

Flow Physics and Technology

Research Group

Wind Energy

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.