The finite cell method is an embedded domain method, which combines the fictitious domain
approach with higher-order finite elements, adaptive integration, and weak enforcement of …

This paper presents the basic concepts and the module structure of the Distributed and
Unified Numerics Environment and reflects on recent developments and general changes …

In this article we consider finite element methods for approximating the solution of partial
differential equations on surfaces. We focus on surface finite elements on triangulated …

An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical
solution of second-order elliptic partial differential equations on general computational …

We introduce a new class of unfitted finite element methods with high order accurate
numerical integration over curved surfaces and volumes which are only implicitly defined by …

This article presents new immersed finite element (IFE) methods for solving the popular
second order elliptic interface problems on structured Cartesian meshes even if the involved …

Abstract The Shifted Boundary Method (SBM) is an approximate domain method for
boundary value problems, in the broader class of unfitted/embedded/immersed methods …

Abstract The Finite Cell Method (FCM) is an embedded domain method, which combines the
fictitious domain approach with high-order finite elements, adaptive integration, and weak …

Generating finite element discretizations with direct interface parameterizations constitutes a
considerable computational expense in case of complex interface geometries. The paper at …

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