39 citations · 104 across the 28 of their papers we have counts for
29 papers
A Virtual Element Method for elliptic problems on trimmed background meshes
L. Beirão da Veiga, C. Canuto, R. H. Nochetto +2
We consider a two-dimensional piecewise domain that cuts through a quasi-uniform fixed polygonal background mesh, for instance made of quadrilaterals. A simple procedure base…
Pressure and convection robust Finite Elements for Magnetohydrodynamics
L. Beirão da Veiga, F. Dassi, G. Vacca
We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. Both methods employ…
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…
Mixed Virtual Element approximation of linear acoustic wave equation
Franco Dassi, Alessio Fumagalli, Ilario Mazzieri +1
We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method…
Virtual Element Method for the Navier--Stokes Equation coupled with the Heat Equation
Paola Francesca Antonietti, Giuseppe Vacca, Marco Verani
We consider the Virtual Element discretization of the Navier-Stokes equations coupled with the heat equation where the viscosity depends on the temperature. We present the Virtual…
-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration
Paola F. Antonietti, Simone Scacchi, Giuseppe Vacca +1
We consider the -Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we…
Bend 3d Mixed Virtual Element Method for Elliptic Problems
Franco Dassi, Alessio Fumagalli, Anna Scotti +1
In this study, we propose a virtual element scheme to solve the Darcy problem in three physical dimensions. The main novelty, here proposed, is that curved elements are naturally h…
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…
A Virtual Element Method for the wave equation on curved edges in two dimensions
Franco Dassi, Alessio Fumagalli, Ilario Mazzieri +2
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. C…
SUPG-stabilized Virtual Elements for diffusion-convection problems: a robustness analysis
L. Beirão da Veiga, F. Dassi, C. Lovadina +1
The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the conv…
The mixed virtual element method for grids with curved interfaces
Franco Dassi, Alessio Fumagalli, Davide Losapio +3
In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be…
The Mixed Virtual Element Method on curved edges in two dimensions
Franco Dassi, Alessio Fumagalli, Davide Losapio +3
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…
Equilibrium analysis of an immersed rigid leaflet by the virtual element method
L. Beirão da Veiga, C. Canuto, R. H. Nochetto +1
We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a r…
Sharper error estimates for Virtual Elements and a bubble-enriched version
L. Beirao da Veiga, G. Vacca
In the present contribution we develop a sharper error analysis for the Virtual Element Method, applied to a model elliptic problem, that separates the element boundary and element…
A virtual element method for the miscible displacement of incompressible fluids in porous media
Lourenco Beirao da Veiga, Alexander Pichler, Giuseppe Vacca
In the present contribution, we construct a virtual element (VE) discretization for the problem of miscible displacement of one incompressible fluid by another, described by a time…
The Stokes complex for Virtual Elements in three dimensions
L. Beirao da Veiga, F. Dassi, G. Vacca
The present paper has two objectives. On one side, we develop and test numerically divergence free Virtual Elements in three dimensions, for variable ``polynomial'' order. These ar…
The - and -versions of the virtual element method for elliptic eigenvalue problems
O. Certik, F. Gardini, G. Manzini +2
We discuss the - and the -versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An appl…
Bricks for the mixed high-order virtual element method: projectors and differential operators
Franco Dassi, Giuseppe Vacca
We present the essential instruments to deal with Virtual Element Method (VEM) for the resolution of partial differential equations in mixed form. Functional spaces, degrees of fre…
The Stokes complex for Virtual Elements with application to Navier--Stokes flows
L. Beirão da Veiga, D. Mora, G. Vacca
In the present paper, we investigate the underlying Stokes complex structure of the Virtual Element Method for Stokes and Navier--Stokes introduced in previous papers by the same a…
The virtual element method for eigenvalue problems with potential terms on polytopal meshes
Ondrej Certik, Francesca Gardini, Gianmarco Manzini +1
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the…
The nonconforming virtual element method for eigenvalue problems
Francesca Gardini, Gianmarco Manzini, Giuseppe Vacca
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the tw…
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…
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.…