37 citations · 125 across the 22 of their papers we have counts for
24 papers
A Virtual Element method for non-Newtonian fluid flows
P. F. Antonietti, L. Beirao da Veiga, M. Botti +2
In this paper, we design and analyze a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the…
A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection
Lourenço Beirão da Veiga, Daniele A. Di Pietro, Kirubell B. Haile
We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and -type diffusion, with Sobolev indices . The discretization of the d…
CIP-stabilized Virtual Elements for diffusion-convection-reaction problems
L. Beirao da Veiga, C. Lovadina, M. Trezzi
The Virtual Element Method for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous…
Robust Finite Elements for linearized Magnetohydrodynamics
L. Beirão da Veiga, F. Dassi, G. Vacca
We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presenc…
Adaptive VEM for variable data: convergence and optimality
L. Beirão da Veiga, C. Canuto, R. H. Nochetto +2
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization…
Pressure robust SUPG-stabilized finite elements for the unsteady Navier-Stokes equation
L. Beirão da Veiga, F. Dassi, G. Vacca
In the present contribution we propose a novel conforming Finite Element scheme for the time-dependent Navier-Stokes equation, which is proven to be both convection quasi-robust an…
A fully-discrete virtual element method for the nonstationary Boussinesq equations
L. Beirão da Veiga, D. Mora, A. Silgado
In the present work we propose and analyze a fully coupled virtual element method of high order for solving the two dimensional nonstationary Boussinesq system in terms of the stre…
The Virtual Element Method for the 3D Resistive Magnetohydrodynamic model
Lourenço Beirão da Veiga, Franco Dassi, Gianmarco Manzini +1
We present a four-field Virtual Element discretization for the time-dependent resistive Magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete form…
Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
Lourenço Beirão da Veiga, Franco Dassi, Daniele A. Di Pietro +1
This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equat…
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property
L. Beirao da Veiga, C. Canuto, R. H. Nochetto +2
In the present paper we initiate the challenging task of building a mathematically sound theory for Adaptive Virtual Element Methods (AVEMs). Among the realm of polygonal meshes, w…
Interpolation and stability properties of low order face and edge virtual element spaces
Lourenço Beirão da Veiga, Lorenzo Mascotto
We analyse the interpolation properties of 2D and 3D low order virtual element face and edge spaces, which generalize Nédélec and Raviart-Thomas polynomials to polygonal-polyhedral…
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…
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…
Virtual Elements for a shear-deflection formulation of Reissner-Mindlin plates
Lourenço Beirão da Veiga, David Mora, Gonzalo Rivera
We present a virtual element method for the Reissner-Mindlin plate bending problem which uses shear strain and deflection as discrete variables without the need of any reduction op…
Virtual Elements for the Navier-Stokes problem on polygonal meshes
L. Beirão da Veiga, C. Lovadina, G. Vacca
A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free.…
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…
Divergence free Virtual Elements for the Stokes problem on polygonal meshes
L. Beirao da Veiga, C. Lovadina, G. Vacca
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 associate…
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…
Mimetic Finite Difference methods for Hamiltonian wave equations in 2D
Lourenco Beirao da Veiga, Luciano Lopez, Giuseppe Vacca
In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimension. We use the Mimetic Finite Difference (MFD) method to approximate the con…
A virtual element method for the Cahn-Hilliard equation with polygonal meshes
Paola F. Antonietti, Lourenco Beirao da Veiga, Simone Scacchi +1
In this paper we develop an evolution of the virtual elements of minimal degree for the approximation of the Cahn-Hilliard equation. The proposed method has the advantage of…
A family of C^0 finite elements for Kirchhoff plates I: Error analysis
L. Beirao da Veiga, J. Niiranen, R. Stenberg
A new finite element formulation for the Kirchhoff plate model is presented. The method is a displacement formulation with the deflection and the rotation vector as unknowns and it…