This paper surveys the construction, properties, and applications of generalized barycentric
coordinates on polygons and polyhedra. Applications include: surface mesh parametrization …

We analyze the virtual element methods (VEM) on a simple elliptic model problem, allowing
for more general meshes than the one typically considered in the VEM literature. For …

We consider the discretization of a boundary value problem for a general linear second-
order elliptic operator with smooth coefficients using the Virtual Element approach. As in [AH …

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 …

The present work deals with the formulation of a virtual element method for two dimensional
structural problems. The contribution is split in two parts: in part I, the elastic problem is …

In the present paper we introduce a Virtual Element Method (VEM) for the approximate
solution of general linear second order elliptic problems in mixed form, allowing for variable …

This paper provides brief review on polygonal/polyhedral finite elements. Various
techniques, together with their advantages and disadvantages, are listed. A comparison of …

Generalized barycentric coordinates such as Wachspress and mean value coordinates have
been used in polygonal and polyhedral finite element methods. Recently, mimetic finite …

The numerical approximation of 2D elasticity problems is considered, in the framework of the
small strain theory and in connection with the mixed Hellinger–Reissner variational …

The focus of this paper is on develo** a virtual element method (VEM) for Darcy and
Brinkman equations. In [L. Beirão da Veiga, C. Lovadina and G. Vacca, ESAIM Math. Model …