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 …

Embedded or immersed boundary methods (IBM) are powerful mesh-based techniques that
permit to solve partial differential equations (PDEs) in complex geometries circumventing the …

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

Embedded and immersed methods have become essential tools in computational
mechanics, as they allow discretizing arbitrarily complex geometries without the need for …

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 …

This article documents a cut‐cell finite element method for solving Poisson's equation in
smooth three‐dimensional domains using a uniform, Cartesian axis‐aligned grid. Neumann …

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

We conduct a condition number analysis of a Hybrid High-Order (HHO) scheme for the
Poisson problem. We find the condition number of the statically condensed system to be …

To facilitate widespread adoption of automated engineering design techniques, existing
methods must become more efficient and generalizable. In the field of topology optimization …

Surface/surface intersection is a fundamental problem in Compute Aided Design and
Geometric Modeling since it is essential to solid modeling, numerically controlled machining …