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 consider the reliable implementation of high-order unfitted finite element methods on
Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable …

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

Multi-material problems often exhibit complex geometries along with physical responses
presenting large spatial gradients or discontinuities. In these cases, providing high-quality …

We propose a space-time scheme that combines an unfitted finite element method in space
with a discontinuous Galerkin time discretisation for the accurate numerical approximation of …

We present a novel stabilized isogeometric formulation for the Stokes problem, where the
geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) …

We develop a discrete extension operator for trimmed spline spaces consisting of piecewise
polynomial functions of degree p with k continuous derivatives. The construction is based on …

We present a new high-order spectral element solution to the two-dimensional scalar
Poisson equation subject to a general Robin boundary condition. The solution is based on a …

This work proposes a novel variational approximation of partial differential equations on
moving geometries determined by explicit boundary representations. The benefits of the …

A high-order, degree-adaptive hybridizable discontinuous Galerkin (HDG) method is
presented for two-fluid incompressible Stokes flows, with boundaries and interfaces …