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 …

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 …

About 10 years ago, Mixed and Hybrid Finite Element Methods by F. Brezzi and M. Fortin
went out of print and we were asked to allow a second printing. The world had evolved and …

The Hitchhiker's Guide to the Virtual Element Method | Mathematical Models and Methods in
Applied Sciences World Scientific Search This Journal Anywhere Quick Search in Journals …

In the present paper we develop a new family of Virtual Elements for the Stokes problem on
polygonal meshes. By a proper choice of the Virtual space of velocities and the associated …

A family of virtual element methods for the two-dimensional Navier--Stokes equations is
proposed and analyzed. The schemes provide a discrete velocity field which is pointwise …

This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …

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

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …

We discuss the application of Virtual Elements to linear plate bending problems, in the
Kirchhoff–Love formulation. As we shall see, in the Virtual Element environment the …