This book provides a self-contained introduction to the simulation of flow and transport in
porous media, written by a developer of numerical methods. The reader will learn how to …

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 …

The problem of contact between two elastic bodies is addressed computationally using the
virtual element method (VEM). The use of the VEM allows the use of non-matching meshes …

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 …

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 …

Abstract We present a Virtual Element Method (VEM) for possibly nonlinear elastic and
inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is …

We present, in a unified framework, new conforming and nonconforming virtual element
methods for general second-order elliptic problems in two and three dimensions. The …

We present a general virtual element method (VEM) framework for finite elasticity, which
emphasizes two issues: element-level volume change (volume average of the determinant …

In this paper we develop an evolution of the C^1 virtual elements of minimal degree for the
approximation of the Cahn--Hilliard equation. The proposed method has the advantage of …