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 …

When dealing with multirotor devices such as quadcopters or wind farms, the cost of blade-
resolved large-eddy simulation (LES) becomes prohibitive. Combining LES with a family of …

In this work, we analyse the links between ghost penalty stabilisation and aggregation-
based discrete extension operators for the numerical approximation of elliptic partial …

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG)
framework is developed for fluid interface dynamics, facilitating precise computation of …

In this paper, we develop a high-order method for the steady two-phase compressible
Navier–Stokes equations closed by generic equations of state, adapted to gas–liquid flows …

In the last decade, there has been a lot of interest in develo** high-order methods as a
viable option for unsteady scale-resolving-simulations which are increasingly important in …

In this work, we propose a novel formulation for the solution of partial differential equations
using finite element methods on unfitted meshes. The proposed formulation relies on the …

We develop a stabilized cut discontinuous Galerkin framework for the numerical solution of
elliptic boundary value and interface problems on complicated domains. The domain of …

In this paper we present a robust remeshing-free cutting algorithm on the basis of the
eXtended Finite Element Method (XFEM) and fully implicit time integration. One of the most …

When modeling scientific and industrial problems, geometries are typically modeled by
explicit boundary representations obtained from computer-aided design software. Unfitted …