Stability and conditioning of immersed finite element methods: analysis and remedies

Frits de Prenter, Clemens Verhoosel, Harald van Brummelen, Mats Larson, Santiago Badia

Research output: Contribution to journalReview articlepeer-review

9 Citations (Scopus)
78 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)3617-3656
Number of pages40
JournalArchives of Computational Methods in Engineering
Issue number6
Publication statusPublished - 2023


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