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 …

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

Ill-conditioning of the system matrix is a well-known complication in immersed finite element
methods and trimmed isogeometric analysis. Elements with small intersections with the …

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 …

Immersed finite element methods generally suffer from conditioning problems when cut
elements intersect the physical domain only on a small fraction of their volume. We present a …

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

This chapter reviews the work conducted by our team on scan-based immersed
isogeometric analysis for flow problems. To leverage the advantageous properties of …

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

We develop a general framework for construction and analysis of discrete extension
operators with application to unfitted finite element approximation of partial differential …

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