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 …

Fluid flow applications can involve a number of coupled problems. One is the simulation of
free-surface flows, which require the solution of a free-boundary problem. Within this …

This study focuses on finding the optimal layout of fluidic devices subjected to
incompressible flow at low Reynolds numbers. The proposed approach uses a levelset …

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

The extended finite element method (XFEM) is frequently used in order to incorporate
discontinuous solution properties into the approximation space. Discontinuities inside …

We present a positivity preserving variational scheme for the phase-field modeling of
incompressible two-phase flows with high density ratio. The variational finite element …

Before proceeding with the variational formulation of the fluid-structure coupled system, let
us look at the convection-diffusion-reaction (CDR) equation which forms a canonical …

We develop a new stabilized XFEM based fixed-grid approach for the transient
incompressible Navier–Stokes equations using cut elements. Our framework is based on a …

A novel extended variational multiscale method for incompressible two‐phase flow is
proposed. In this approach, the level‐set method, which allows for accurately representing …

This paper shows an inf-sup stability property for several well-known 2D and 3D Stokes
elements on triangulations which are not fitted to a given smooth or polygonal domain. The …