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 …

We propose new quadrature schemes that asymptotically require only four in-plane points
for Reissner–Mindlin shell elements and nine in-plane points for Kirchhoff–Love shell …

In the first part of this chapter the basic algorithmic structure and performance characteristics
of the p-version of the finite element method are surveyed with reference to elliptic problems …

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the
phase-field approach for fracture by modeling the crack as a diffusive object being described …

Fictitious domain methods, such as the finite cell method, simplify the discretization of a
domain significantly. This is because the mesh does not need to conform to the domain of …

This publication presents a robust and efficient approach for fully CAD-integrated analyses
of solids, which aims to reduce the current modeling effort for static and transient problems …

An accurate implicit description of geometries is enabled by the level-set method. Level-set
data is given at the nodes of a higher-order background mesh and the interpolated zero …

This work proposes two efficient quadrature rules, reduced Gauss quadrature and Gauss–
Greville quadrature, for isogeometric analysis. The rules are constructed to exactly integrate …

Abstract The Cut Finite Element Method (CutFEM) is recently shown to be a versatile
approach for tunnel construction modeling and settlement analysis. The CutFEM can …

Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and
accurate simulation of complex geometries by utilizing higher-order shape functions and an …