Unfitted finite element techniques are valuable tools in different applications where the
generation of body-fitted meshes is difficult. However, these techniques are prone to severe …

In the first part of this chapter the basic algorithmic structure and performance characteristics
of the p-version of the finite element method are surveyed with reference to elliptic problems …

We present a 50-line MATLAB implementation of the lowest order virtual element method for
the two-dimensional Poisson problem on general polygonal meshes. The matrix formulation …

We present a method for the numerical integration of homogeneous functions over convex
and nonconvex polygons and polyhedra. On applying Stokes's theorem and using the …

We present a higher order discretization scheme for the compressible Euler and Navier–
Stokes equations with immersed boundaries. Our approach makes use of a discontinuous …

Fictitious domain methods, such as the Finite Cell Method (FCM), allow for an efficient and
accurate simulation of complex geometries by utilizing higher-order shape functions and an …

Mortar finite element methods provide a very convenient and powerful discretization
framework for geometrically nonlinear applications in computational contact mechanics …

We show both theoretically and numerically a connection between the smoothed finite
element method (SFEM) and the virtual element method and use this approach to derive …

We present a novel method to perform numerical integration over curved polyhedra
enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a …

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 …