TY - JOUR
T1 - Stability and Conditioning of Immersed Finite Element Methods
T2 - Analysis and Remedies
AU - de Prenter, Frits
AU - Verhoosel, Clemens V.
AU - van Brummelen, E. Harald
AU - Larson, Mats G.
AU - Badia, Santiago
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/7
Y1 - 2023/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85159711652&partnerID=8YFLogxK
U2 - 10.1007/s11831-023-09913-0
DO - 10.1007/s11831-023-09913-0
M3 - Review Article
AN - SCOPUS:85159711652
SN - 1134-3060
VL - 30
SP - 3617
EP - 3656
JO - Archives of Computational Methods in Engineering
JF - Archives of Computational Methods in Engineering
IS - 6
ER -