Explanipedia

Second order three-dimensional serendipity virtual elements for hyperelasticity: Static and dynamic analysis Open

Bing‐Bing Xu, L. Beirão da Veiga, Yongjie Zhang, Peter Wriggers · 2025

Mesh generation of curvilinear polygons for the high-order virtual element method (VEM) Open

Kaloyan S. Kirilov, Jingtian Zhou, Joaquim Peiró, Mashy Green, David Moxey , et al. · 2025

Fully and semi-implicit robust space–time DG methods for the incompressible Navier–Stokes equations Open

Luís Veiga, Sergio Gómez, Franco Dassi · 2025

We carry out a stability and convergence analysis of a fully discrete scheme for the time-dependent Navier–Stokes equations resulting from combining an [Formula: see text]-conforming discontinuous Galerkin spatial discretization, and a dis…

Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system Open

L. Beirão da Veiga, Kaibo Hu, Lorenzo Mascotto · 2025

We derive error estimates of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of the system, and the magnetic and cross helicities on the d…

SUPG-stabilized time-DG finite and virtual elements for the time-dependent advection–diffusion equation Open

L. Beirão da Veiga, Franco Dassi, Sergio Gómez · 2025

We carry out a stability and convergence analysis for the fully discrete scheme obtained by combining a finite or virtual element spatial discretization with the upwind-discontinuous Galerkin time-stepping applied to the time-dependent adv…

SUPG-stabilized time-DG finite and virtual elements for the time-dependent advection-diffusion equation Open

L. Beirão da Veiga, Franco Dassi, Sergio Gómez · 2024

We carry out a stability and convergence analysis for the fully discrete scheme obtained by combining a finite or virtual element spatial discretization with the upwind-discontinuous Galerkin time-stepping applied to the time-dependent adv…

$C^1$ virtual element methods on polygonal meshes with curved edges Open

L. Beirão da Veiga, D. Mora, Alberth Silgado · 2024

In this work we design a novel $C^1$-conforming virtual element method of arbitrary order $k \geq 2$, to solve the biharmonic problem on a domain with curved boundary and internal curved interfaces in two dimensions. By introducing a suita…

A Virtual Element method for non-Newtonian pseudoplastic Stokes flows Open

Paola F. Antonietti, L. Beirão da Veiga, Michele Botti, Giuseppe Vacca, Marco Verani · 2024

In this paper, we design and analyze a Virtual Element discretization for the steady motion of non -Newtonian pseudoplastic, incompressible Stokes fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness propert…

CIP-stabilized virtual elements for diffusion-convection-reaction problems Open

L. Beirão da Veiga, Carlo Lovadina, Manuel Trezzi · 2024

The Virtual Element Method (VEM) for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous Interior Penalty approach is employed. Due to the pre…

A Péclet-robust Discontinuous Galerkin method for nonlinear diffusion with advection Open

L. Beirão da Veiga, Daniele A. Di Pietro, Kirubell B. Haile · 2024

We analyze a Discontinuous Galerkin method for a problem with linear advection–reaction and [Formula: see text]-type diffusion, with Sobolev indices [Formula: see text]. The discretization of the diffusion term is based on the full gradien…

Pressure and convection robust Finite Elements for Magnetohydrodynamics Open

L. Beirão da Veiga, Franco Dassi, Giuseppe Vacca · 2024

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 the $H_{\rm div}$ conforming BDM element coupled with an a…

The Nonconforming Virtual Element Method with Curved Edges Open

L. Beirão da Veiga, Yi Liu, Lorenzo Mascotto, Alessandro Russo · 2024

A Virtual Element method for non-Newtonian fluid flows Open

Paola F. Antonietti, L. Beirão da Veiga, Michela Botti, Giuseppe Vacca, Marco Verani · 2024

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 monotonicity and boundedness properties of the continuous …

A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection Open

L. Beirão da Veiga, Daniele A. Di Pietro, Kirubell B. Haile · 2024

We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and $p$-type diffusion, with Sobolev indices $p\in (1, \infty)$. The discretization of the diffusion term is based on the full gradient including jump …

Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes with arbitrary regular solution. Open

Gianmarco Manzini, L. Beirão da Veiga · 2024

A Virtual Element Method for Non-Newtonian Fluid Flows Open

Paola F. Antonietti, L. Beirão da Veiga, Michele Botti, Giuseppe Vacca, Marco Verani · 2024

Supg-Stabilized Time-Dg Finite and Virtual Elements for the Time-Dependent Advection-Diffusion Equation Open

L. Beirão da Veiga, Franco Dassi, Sergio Gómez · 2024

CIP-stabilized Virtual Elements for diffusion-convection-reaction problems Open

L. Beirão da Veiga, Carlo Lovadina, Manuel Trezzi · 2023

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 Interior Penalty approach is employed. Due to the presence …

Robust Finite Elements for linearized Magnetohydrodynamics Open

L. Beirão da Veiga, Franco Dassi, Giuseppe Vacca · 2023

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 presence of high fluid and magnetic Reynolds numbers. The proposed…

The virtual element method Open

L. Beirão da Veiga, Franco Brezzi, L. D. Marini, A. Russo · 2023

The present review paper has several objectives. Its primary aim is to give an idea of the general features of virtual element methods (VEMs), which were introduced about a decade ago in the field of numerical methods for partial different…

The virtual element method for a 2D incompressible MHD system Open

Sebastián Naranjo Álvarez, L. Beirão da Veiga, Vrushali A. Bokil, Franco Dassi, Vitaliy Gyrya , et al. · 2023

The nonconforming virtual element method with curved edges Open

L. Beirão da Veiga, Yi Liu, Lorenzo Mascotto, Alessandro Russo · 2023

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 in the energy and $L^2$ norms, and validate the theoretical …

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

L. Beirão da Veiga, Claudio Canuto, Ricardo H. Nochetto, Giuseppe Vacca, Marco Verani · 2023

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, we restrict our analysis to triangular meshes with hanging n…

Stability and interpolation properties of serendipity nodal virtual elements Open

L. Beirão da Veiga, Lorenzo Mascotto · 2023

We discuss stability and interpolation properties of serendipity nodal virtual element spaces in two and three dimensions. Notably, we rigorously prove stability bounds for the “dofi-dofi” stabilization and show that the best interpolation…

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

L. Beirão da Veiga, F. Dassi, G. Vacca · 2023

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 and pressure robust. The method is built combining a "diverge…

Adaptive VEM for variable data: convergence and optimality Open

L. Beirão da Veiga, C. Canuto, R. H. Nochetto, G. Vacca, M. Verani · 2023

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-free a posteriori error estimators recently derived in [8]…

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

L. Beirão da Veiga, David Mora, Alberth Silgado · 2023

Stability and Interpolation Properties for Stokes-Like Virtual Element Spaces Open

Jian Meng, L. Beirão da Veiga, Lorenzo Mascotto · 2023

The virtual element method for the 3D resistive magnetohydrodynamic model Open

L. Beirão da Veiga, Franco Dassi, Gianmarci Manzini, Lorenzo Mascotto · 2023

We present a four-field virtual element discretization for the time-dependent resistive magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral mes…

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

L. Beirão da Veiga, Lorenzo Mascotto · 2023

We analyse the interpolation properties of two-dimensional and three-dimensional low-order virtual element (VE) face and edge spaces, which generalize Nédélec and Raviart–Thomas polynomials to polygonal-polyhedral meshes. Moreover, we inve…

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