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.@en

With 66 participants from 14 countries, the 3rd Conference on Isogeometric Analysis and Applications 2018 was a successful continuation of the IGAA conference series that was started in 2012 in Linz, Austria and had its second edition in 2014 in Annweiler am Trifels, Germany. IGAA 2018 has brought together senior experts from academia and industry as well as young scientists standing at the beginning of their career to discuss the current state of the art in IGA and its potential for commercial application in industry. This book contains a selection of 12 papers addressing various aspects of IGA ranging from the mathematical analysis of approximation properties over the generation of analysis-suitable parametrizations and the efficient solution of linear systems of equations, to its use in practical applications. A conference like IGAA cannot be organized without external support. The organizers would like to thank the 4TU Applied Mathematics Institute (4TU.AMI), the TU Delft Institute for Computational Science and Engineering (DCSE), the J.M. Burgerscentrum, and the NWO Cluster Nonlinear Dynamics of Natural Systems (NDNS+) for generous financial support. Financial support from the European Commission through project MOTOR (GA no. 678727) is also greatly acknowledged. We finally would like to express our gratitude to Mrs. Deborah Dongor and her colleagues for taking care of the local organization of this event. @en