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 …

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 …

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 …

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 …

We present a tetrahedral finite cell method for the simulation of incompressible flow around
geometrically complex objects. The method immerses such objects into non-boundary-fitted …

Discretization methods based on meshes that do not conform to the geometry of the problem
under consideration require special treatment when it comes to the integration of finite …

In this contribution, a novel framework for simulating mixed-mode failure in rock is
presented. Based on a hybrid phase-field model for mixed-mode fracture, separate phase …

Abstract In Selective Laser Melting (SLM) processes, residual stress formation can
substantially affect mechanical properties and geometric accuracy of the produced part. The …

A fast and simple grid generation can be achieved by non-standard discretization methods
where the mesh does not conform to the boundary or the internal interfaces of the problem …

This work presents an h-adaptive finite-element (FE) strategy to address the numerical
simulation of additive manufacturing (AM) of large-scale parts. The wire-arc additive …