62 citations · 210 across the 18 of their papers we have counts for
21 papers
Conforming/Non-conforming Virtual Elements and application to elasticity problems in curved three-dimensional domains
L. Beirão da Veiga, F. Dassi, A. Russo +1
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel…
Quantitative study of the stabilization parameter in the virtual element method
Alessandro Russo, N. Sukumar
The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabili…
The nonconforming virtual element method with curved edges
Lourenco Beirão Da Veiga, Yi Liu, Lorenzo Mascotto +1
We introduce a nonconforming virtual element method for the Poisson equation on domains with curved boundary and internal interfaces. We prove arbitrary order optimal convergence i…
Virtual Elements and curved edges
L. Beirao Da Veiga, F. Brezzi, L. D. Marini +1
We present a new method to construct Virtual Element spaces on polygons with curved edges.
Virtual Element Method on polyhedral meshes
Lourenco Beirão da Veiga, Franco Dassi, Alessandro Russo
The purpose of the present paper is to develop Virtual Elements in three dimensions for linear elliptic fourth order problems, motivated by the difficulties that standard con…
A family of three-dimensional virtual elements with applications to magnetostatic
L. Beirão da Veiga, F. Brezzi, F. Dassi +2
We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In…
The Virtual Element Method with curved edges
L. Beirão da Veiga, A. Russo, G. Vacca
In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approxima…
Serendipity Virtual Elements on Polyhedral Meshes
Lourenco Beirao da Veiga, Franco Brezzi, Franco Dassi +2
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 nu…
Lowest order Virtual Element approximation of magnetostatic problems
L. Beirão da Veiga, F. Brezzi, F. Dassi +2
We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in thre…
Veamy: an extensible object-oriented C++ library for the virtual element method
Alejandro Ortiz-Bernardin, Catalina Alvarez, Nancy Hitschfeld-Kahler +3
This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on…
High-order Virtual Element Method on polyhedral meshes
L. Beirão da Veiga, F. Dassi, A. Russo
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 dimens…
Exponential convergence of the hp Virtual Element Method with corner singularities
Lorenzo Mascotto, Lourenço Beirão da Veiga, Alexey Chernov +1
In the present work, we analyze the version of Virtual Element methods for the 2D Poisson problem. We prove exponential convergence of the energy error employing sequences of…
Stability Analysis for the Virtual Element Method
Lourenco Beirao da Veiga, Carlo Lovadina, Alessandro Russo
We analyse 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 insta…
Serendipity Face and Edge VEM Spaces
L. Beirao da Veiga, F. Brezzi, L. D. Marini +1
We extend the basic idea of Serendipity Virtual Elements from the previous case (by the same authors) of nodal (-conforming) elements, to a more general framework. Then we app…
Serendipity Nodal VEM spaces
L. Beirao da Veiga, F. Brezzi, L. D. Marini +1
We introduce a new variant of Nodal Virtual Element spaces that mimics the "Serendipity Finite Element Methods" (whose most popular example is the 8-node quadrilateral) and allows…
Basic principles of hp Virtual Elements on quasiuniform meshes
L. Beirão da Veiga, A. Chernov, L. Mascotto +1
In the present paper we initiate the study of Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimate…
Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes
L. Beirao da Veiga, F. Brezzi, L. D. Marini +1
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…
A Plane Wave Virtual Element Method for the Helmholtz Problem
Ilaria Perugia, Paola Pietra, Alessandro Russo
We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict…
Virtual Element Methods for general second order elliptic problems on polygonal meshes
L. Beirão da Veiga, F. Brezzi, L. D. Marini +1
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 [5…
H(div) and H(curl)-conforming VEM
L. Beirao da Veiga, F. Brezzi, L. D. Marini +1
In the present paper we construct Virtual Element Spaces that are -conforming and -conforming on general polygonal and polyhedral elements; these s…
Preconditioned HSS Method for Finite Element Approximations of Convection-Diffusion Equations
Alessandro Russo, Cristina Tablino Possio
A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element…