Related papers: The Virtual Element Method in 50 lines of MATLAB
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
We analyze in this paper a virtual element approximation for the acoustic vibration problem. We consider a variational formulation relying only on the fluid displacement and propose a discretization by means of H(div) virtual elements with…
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…
The Virtual Element Method (VEM) is used to perform the discretization of the Poisson problem on polygonal and polyhedral meshes. This results in a symmetric positive definite linear system, which is solved iteratively using overlapping…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…
We develop a lowest-order nonconforming virtual element method for planar linear elasticity, which can be viewed as an extension of the idea in Falk (1991) to the virtual element method (VEM), with the family of polygonal meshes satisfying…
In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics,…
We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However,…
A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…
We numerically validate the Virtual Element Method of order k for general second order elliptic problems with variable coefficients in three dimensions. Moreover, we investigate numerically also the Serendipity version of the VEM (in three…
In this paper, we employ the techniques developed for second order operators to obtain the new estimates of Virtual Element Method for fourth order operators. The analysis is based on elements with proper shape regularity. Estimates for…
Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable…
In this paper, we investigate a sixth order elliptic equation with the simply supported boundary conditions in a polygonal domain. We propose a new method that decouples the sixth order problem into a system of second order equations.…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
This paper presents two approaches: the virtual element method (VEM) and the stabilization-free virtual element method (SFVEM) for analyzing thermomechanical behavior in electronic packaging structures with geometric multi-scale features.…