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 …

We review the treatment of trimmed geometries in the context of design, data exchange, and
computational simulation. Such models are omnipresent in current engineering modeling …

We discuss recent advances on robust unfitted finite element methods on cut meshes. These
methods are designed to facilitate computations on complex geometries obtained, for …

We extend the classical Nitsche type weak boundary conditions to a fictitious domain setting.
An additional penalty term, acting on the jumps of the gradients over element faces in the …

Nitsche's method can be used as a coupling tool for non-matching discretizations by weakly
enforcing interface constraints. We explore the use of weak coupling based on Nitsche's …

We present a finite element method for the Stokes equations involving two immiscible
incompressible fluids with different viscosities and with surface tension. The interface …

Enforcing essential boundary conditions plays a central role in immersed boundary
methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and …

Thin shell structures are widely used in the aerospace, automotive and mechanical
engineering industries. They are ideal candidates for the isogeometric analysis paradigm …

In this work, we propose a stabilized explicit coupling scheme for fluid–structure interaction
problems involving a viscous incompressible fluid. The coupled discrete formulation is …

A new adaptive refinement strategy for phase-field models of brittle fracture is proposed. The
approach provides a computationally efficient solution to the high demand in spatial …