Publications

P. F. Antonietti, G. Vacca, M. Verani 

Virtual Element Method for the Navier–Stokes Equation coupled with the Heat Equation. 

IMA Journal of Numerical Analysis

A. Lamperti, M. Cremonesi, U. Perego, A. Russo, C. Lovadina

A Hu–Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics

Computational Mechanics

L. Mascotto

The role of stabilization in the virtual element method: a survey

Computers & Mathematics with Applications

L. Beirão da Veiga, D. Mora, A. Silgado

A fully-discrete virtual element method for the nonstationary Boussinesq equations in stream-function form

Comp. Meth. Appl. Mech. Engrg

L. Beirão da Veiga, L. Mascotto. 

Stability and interpolation properties of serendipity nodal virtual elements

Appl. Math

L. Beirão da Veiga, L. Mascotto

Interpolation and stability properties of low order face and edge virtual element spaces

IMA Journal of Numerical Analysis

J. Meng, L. Beirão da Veiga, L. Mascotto

Stability and interpolation properties for Stokes-like virtual element spaces

J. of Sci. Comp.

L. Beirão da Veiga, F. Brezzi, L.D. Marini, A Russo. 

The virtual element method

ACTA Numerica

L. Beirão da Veiga, C. Canuto, R.H. Nochetto, G. Vacca, M. Verani. 

Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property

Siam J. Numer. Anal.

F. Dassi, A. Fumagalli, I. Mazzieri and G. Vacca

Mixed Virtual Element approximation of linear acoustic wave equation

IMA Journal of Numerical Analysis

S. Naranjo-Alvarez, L. Beirão da Veiga, V.A. Bokil , F. Dassi, V. Gyrya, G. Manzini

The virtual element method for a 2D incompressible MHD system

Mathematics and Computers in Simulation

L. Beirão da Veiga, F. Dassi, G. Manzini and L. Mascotto

The virtual element method for the 3D resistive magnetohydrodynamic mode

Math. Mod. and Meth. Appl. Sci.

N. A. Barnafi, F. Dassi, S. Scacchi

Parallel block preconditioners for virtual element discretizations of the time-dependent Maxwell equations

Journal of Computational Physics.

L. Beirão da Veiga, F. Dassi, G. Vacca. 

Pressure robust SUPG-stabilized finite elements for the unsteady Navier–Stokes equation, 

IMA J. Numer. Anal.

Z. Dong, L. Mascotto

hp-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem

Journal of Scientific Computing

L. Beirão da Veiga and G. Vacca

Sharper error estimates for Virtual Elements and a bubbleenriched version

SIAM Journal Numerical Analysis

L. Beirão da Veiga, F. Dassi, G. Manzini, L. Mascotto

Virtual elements for Maxwell's equations

Computers & Mathematics with Applications

F. Dassi, J. Gedicke, L. Mascotto

Adaptive virtual element methods with equilibrated fluxes

Applied Numerical Mathematics

L. Beirão da Veiga, L. Mascotto, J. Meng

Interpolation and stability estimates for edge and face virtual elements of general order

Mathematical Models and Methods in Applied Sciences

P.F. Antonietti, F.Dassi and E. Manuzzi

Machine learning based refinement strategies for polyhedral grids with applications to virtual element and polyhedral discontinuous Galerkin methods

Journal of Computational Physics.

F. Dassi and I. Velásquez

Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems

Computers & Mathematics with Applications.

F. Dassi, A. Fumagalli, A. Scotti and G. Vacca, 

Bend 3d mixed virtual element method for Darcy problems

Computers & Mathematics with Applications.

L. Beirão da Veiga, F. Dassi, D. A. Di Pietro and J. Droniouc

Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes

Computer Methods in Applied Mathematics and Engineering

F. Dassi, P. Di Barba and A. Russo,

A free-cutting mesh strategy for optimal shape synthesis in magnetics

IET Science, Measurement & Technology

F. Dassi, P. Di Barba and A. Russo

Virtual Element Method and Optimal Shape Design in Magnetics

IEEE Transactions on Magnetics

F. Dassi, S. Zampini and S. Scacchi, 

Robust and scalable adaptive BDDC preconditioners for virtual element discretizations of elliptic partial differential equations in mixed form

Computer Methods in Applied Mathematics and Engineering

P. F. Antonietti, L. Mascotto, M. Verani, S. Zonca

Stability analysis of polytopic Discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems,

Journal of Scientific Computing

Ch. Erath, L. Mascotto, J. M. Melenk, I. Perugia, A. Rieder

Mortar coupling of hp-discontinuous Galerkin and boundary element methods for the Helmholtz equation,

Journal of Scientific Computing.

F. Dassi, J. M. Kross, L. Gerardo-Giorda and S. Perotto, 

A denoising tool for the reconstruction of cortical geometries from MRI,

Mathematics and Computers in Simulation.

E. Artioli, L. Mascotto,

Enrichment of the nonconforming virtual element method with singular functions,

Computer Methods in Applied Mechanics and Engineering.

A. Chernov, C. Marcati, L. Mascotto,

p- and hp-virtual elements for the Stokes problem,

Advances in Computational Mathematics.

L. Beirão da Veiga, A. Pichler, G. Vacca, 

A virtual element method for the miscible displacement of incompressible fluids in porous media, 

Computer Methods in Applied Mechanics and Engineering.

L. Beirão da Veiga, C. Canuto, R. H. Nochetto, G. Vacca, 

Equilibrium analysis of an immersed rigid leaflet by the virtual element method, 

Mathematical Models and Methods in Applied Sciences.

F. Dassi, A. Fumagalli, I. Mazzieri, A. Scotti and G. Vacca, 

A Virtual Element Method for the wave equation on curved edges in two dimensions, 

Journal of Scientific Computing.

F. Dassi, A. Fumagalli, D. Losapio, S. Scialò, A. Scotti and G. Vacca, 

The Mixed Virtual Element Method for Grids with Curved Interfaces in Single-Phase Flow Problems, 

SPE Reservoir Simulation Conference.

L. Beirão da Veiga, F. Dassi, G. Manzini and L. Mascotto, 

Virtual elements for Maxwell's equations, 

Computers & Mathematics with Applications.

F. Dassi, C. Lovadina and M. Visinoni, 

Hybridization of the Virtual Element Method for Linear Elasticity Problems,  

Mathematical Models and Methods in Applied Sciences.

F. Dassi, A. Fumagalli, D. Losapio, S. Scialò, A. Scotti and G. Vacca, 

The mixed Virtual Element Method on curved edges in two dimensions, 

Computer Methods in Applied Mathematics and Engineering.

L. Beirão da Veiga, F. Dassi and G. Vacca, 

Vorticity-Stabilized Virtual Elements for the Oseen Equation, 

Mathematical Models and Methods in Applied Sciences.

L. Beirão da Veiga, F. Dassi, C. Lovadina and G. Vacca, 

SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis, 

Mathematical Modelling and Numerical Analysis.

F. Dassi, P. Di Barba and A. Russo, 

The Virtual Element Method for magnetostatics: Two possible approaches, 

International Compumag Society Newsletter.

Z. Dong, L. Mascotto, O. J. Sutton

Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem

SIAM Journal on Numerical Analysis

L. Mascotto, A. Pichler

Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number

Applied Numerical Mathematics.

O. Certik, F. Gardini, L. Mascotto, G. Manzini, G. Vacca, 

The p- and hp-versions of the virtual element method for elliptic eigenvalue problems, 

Computers & Mathematics with Applications.

F. Dassi and S. Scacchi,

Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems, 

Computer Methods in Applied Mechanics and Engineering.

L. Beirao da Veiga, F. Dassi and G. Vacca,

The Stokes complex for Virtual Elements in three dimensions. 

Mathematical Models and Methods in Applied Sciences.

F. Dassi, C. Lovadina and M. Visinoni, 

A three-dimensional Hellinger–Reissner virtual element method for linear elasticity problems. 

Computer Methods in Applied Mechanics and Engineering.

L. Mascotto, J. M. Melenk, I. Perugia, A. Rieder

FEM-BEM mortar coupling for the Helmholtz equation in three dimensions

Computers & Mathematics with Applications

Z. Dong, L. Mascotto

On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems

14th WCCM-ECCOMAS Congress 2020

A. Chernov, L. Mascotto,

The harmonic virtual element method: stabilization and exponential convergence for the Laplace problem on polygonal domain,

IMA Journal on Numerical Analysis.

L. Mascotto, I. Perugia, A. Pichler,

A nonconforming Trefftz virtual element method for the Helmholtz problem,

Mathematical Models and Methods in Applied Sciences

L. Mascotto, I. Perugia, A. Pichler,

A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects,

Computer Methods in Applied Mechanics and Engineering.

L. Beirão da Veiga, D. Mora, G. Rivera, 

Virtual elements for a shear-deection formulation of Reissner-Mindlin plates, 

Math. Comp.

H. Chi, L. Beirão da Veiga, G.H. Paulino, 

A simple and eective gradient recovery scheme and a posteriori error estimator for the Virtual Element Method (VEM), 

Comput. Meth. Appl. Mech. Engrg.

L. Beirão da Veiga, A. Russo, G. Vacca, 

The Virtual Element Method with curved edges, 

Math. Mod. Numer. Anal. 

L. Beirão da Veiga, G. Manzini, L. Mascotto, 

A posteriori error estimation and adaptivity in hp virtual elements,

 Numer. Math.

L. Beirão da Veiga, D. Mora, G. Vacca, 

The Stokes complex for virtual elements with application to Navier-Stokes flows, 

J. Sci. Comp.

E. Artioli, L. Beirão da Veiga, F. Dassi,

Curvilinear Virtual Elements for 2D solid mechanics applications. 

Computer Methods in Applied Mechanics and Engineering.

F. Dassi, S. Scacchi, 

Parallel solvers for virtual element discretizations of elliptic equations in mixed form, 

Computers & Mathematics with Applications.

L. Beirão da Veiga, F. Dassi and A. Russo,

A C1 Virtual Element Method on polyhedral meshes, 

Computers & Mathematics with Applications

F. Dassi and G. Vacca,

Bricks for the mixed high-order virtual element method: Projectors and differential operators, 

Applied Numerical Mathematics.

L. Mascotto, I. Perugia, A. Pichler

Non-conforming harmonic virtual element method: h- and p-versions

Journal of Scientific Computing 

P. F. Antonietti, L. Mascotto, M. Verani

A multigrid algorithm for the p-version of the virtual element method

ESAIM Mathematical Modelling and Numerical Analysis

L. Mascotto

Ill-conditioning in the virtual element method: stabilizations and bases

Numerical Methods for Partial Differential Equations

L. Beirão da Veiga, C. Lovadina, G. Vacca,

Virtual elements for the Navier-Stokes problem on polygonal meshes,

SIAM J. Numer. Anal..

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L. Beirão da Veiga, A. Chernov, L. Mascotto, A. Russo,

Exponential convergence of the hp virtual element method in presence of corner singularities,

Numer. Math..

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L. Beirão da Veiga, D. Mora, G. Rivera,

Virtual elements for a shear-deflection formulation of Reissner-Mindlin plates,

Math. Comp.

L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini, and A. Russo,

Serendipity virtual elements for general elliptic equations in three dimensions,

Chinese Annals of Mathematics.

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L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini, and  A. Russo,

Lowest order virtual element approximation of magnetostatic problems,

Computer Methods in Applied Mechanics and Engineering.

F. Dassi and L. Mascotto,

Exploring high-order three dimensional virtual elements: Bases and stabilizations,

Computers & Mathematics with Applications.

L. Beirão da Veiga, F. Brezzi, F. Dassi, L. D. Marini, and A. Russo,

A family of three-dimensional virtual elements with applications to magnetostatics, 

SIAM Journal on Numerical Analysis.

B. Dortdivanlioglu, A. Krischok , L. Beirão da Veiga, C. Linder, 

Mixed isogeometric analysis of strongly coupled diffusion in porous materials, 

Int. J. Numer. Meth. Engrng. 

F. Dassi, A. Mola and H. Si, 

Curvature-adapted remeshing of cad surfaces, 

Engineering with Computers.

L. Beirão da Veiga, D. Mora, G. Rivera, R. Rodriguez,

A virtual element method for the acoustic vibration problem,

Numer. Math..

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L. Beirão da Veiga, C. Lovadina, G. Vacca,

Divergence free virtual elements for the Stokes problem on polygonal meshes,

Math. Mod. Numer. Anal.

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H. Chi, L. Beirão da Veiga, G.H. Paulino,

Some basic formulations of the virtual element method (VEM) for finite deformations,

Comput. Meth. Appl. Mech. Engrg.

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E. Artioli, L. Beirão da Veiga, C. Lovadina, E. Sacco,

Arbitrary order 2D virtual elements for polygonal meshes: part I, elastic problem,

Comput. Mech.

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E. Artioli, L. Beirão da Veiga, C. Lovadina, E. Sacco,

Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem,

Comput. Mech.

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L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo,

Serendipity Face and Edge VEM spaces,

Rend. Lincei Math. e Appl.

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L. Beirão da Veiga, C. Lovadina, A. Russo,

Stability analysis for the virtual element method,

Math. Mod. and Meth. Appl. Sci.

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L. Beirão da Veiga, F. Dassi, and A. Russo,

High-order virtual element method on polyhedral meshes,

Computers & Mathematics with Applications.

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L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini, and  A. Russo,

Virtual element approximation of 2d magnetostatic problems,

Computer Methods in Applied Mechanics and Engineering.

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F. Gardini and G. Vacca,

Virtual element method for second-order elliptic eigenvalue problems,

IMA Journal of Numerical Analysis.

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G. Vacca,

An H1-conforming virtual element for Darcy and Brinkman equations,

Mathematical Models and Methods in Applied Sciences.

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A. Ortiz‐Bernardin,  A. Russo  and N. Sukumar,

Consistent and Stable Meshfree Galerkin Methods using the Virtual Element Decomposition,

International Journal for Numerical Methods in Engineering.

L. Beirão da Veiga, L. F. Pavarino,  S. Scacchi, O. Widlund, S. Zampini, 

Adaptive selection of primal constraints for isogeometric BDDC deluxe preconditioners, 

Siam J. Sci. Comp.

F. Auricchio, L. Beirão da Veiga, F. Brezzi, C. Lovadina, 

Mixed Finite Element Methods,

Encyclopedia of Computational Mechanics, Second Edition.

F. Dassi, P. Farrell and H. Si, 

A novel surface remeshing scheme via radial basis functions and higher-dimensional embedding, 

SIAM Journal on Scientific Computing.

F. Dassi, L. Kamenski, P. Farrell and H. Si, 

Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and rbf surface reconstruction, 

Computer-Aided Design.

F. Dassi, S. Perotto, H. Si and T. Streckenbach, 

A priori anisotropic mesh adaptation driven by a higher dimensional embedding, 

Computer-Aided Design.

L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo,

H(div) and H(curl)-conforming virtual element methods,

Numer. Math.

L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo,

Virtual Element Method for general second-order elliptic problems on polygonal meshes,

Math. Models Methods Appl. Sci.

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P. F. Antonietti, L. Beirão da Veiga, S. Scacchi, M. Verani,

A C^1 Virtual Element Method for the Cahn–Hilliard Equation with Polygonal Meshes,

SIAM J. Numer. Anal.

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L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo,

Serendipity Nodal VEM spaces,

Computers & Fluids.

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L. Beirão da Veiga, A. Chernov, L. Mascotto, A. Russo,

Basic principles of hp virtual elements on quasiuniform meshes,

Math. Models Methods Appl. Sci.

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L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo,

Mixed virtual element methods for general second order elliptic problems on polygonal meshes,

Math. Mod. Numer. Anal.

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G. Vacca,

Virtual Element Methods for hyperbolic problems on polygonal meshes.

Computers & Mathematics with Applications.

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I. Perugia, P. Pietra, A. Russo,

A Plane Wave Virtual Element Method for the Helmholtz Problem,

ESAIM: M2AN.

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A. Russo,

On the choice of the internal degrees of freedom for the nodal Virtual Element Method in two dimensions,

Computers & Mathematics with Applications.

F. Dassi, L. Formaggia and S. Zonca.

Degenerate tetrahedra removal, 

Applied Numerical Mathematics..