Compliant mechanisms have become an important branch of modern mechanisms. Unlike
conventional rigid body mechanisms, compliant mechanisms transform the displacement …

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 …

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 …

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 …

We develop a numerical assessment of the Virtual Element Method for the discretization of a
diffusion–reaction model problem, for higher “polynomial” order k and three space …

The present review paper has several objectives. Its primary aim is to give an idea of the
general features of virtual element methods (VEMs), which were introduced about a decade …

Structural optimization is a popular method for designing objects such as bridge trusses,
airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily …

In this work, we develop a general high-order virtual element method for three-dimensional
linear and nonlinear elastic problems. Applications of the virtual element method (VEM) in …

In this study, an efficient polygonal finite element method (PFEM) in combination with
quadratic serendipity shape functions is proposed to study nonlinear static and dynamic …