Franco Brezzi

CNR


Publications

2020, Journal article
Active particles methods and challenges in behavioral systems
N. Bellomo, F. Brezzi, and J. Soler
This paper first provides an introduction to the mathematical approach to the modeling, qualitative analysis, and simulation of large systems of living entities, specifically self-propelled particles....

CNR@People | DOI: 10.1142/S0218202520020017
2019, Journal article
Towards a multiscale vision of active particles
N. Bellomo and F. Brezzi
The aim of this paper is first to provide a presentation of the papers published in a special issue devoted to modeling, qualitative analysis, control and simulations of large systems of living entiti...

CNR@People | DOI: 10.1142/S0218202519020019
2018, Journal article
A family of three-dimensional virtual elements with applications to magnetostatics
L. Beirao Da Veiga, F. Brezzi, F. Dassi, L.D. Marini, and A. Russo
We consider, as a simple model problem, the application of virtual element methods(VEMs) to the linear magnetostatic three-dimensional problem in the formulation of Kikuchi. Indoing so, we also introd...

CNR@People | DOI: 10.1137/18M1169886
2018, Journal article
Challenges in active particles methods: Theory and applications
N. Bellomo and F. Brezzi
This paper is a brief introduction to the mathematical tools employed in the modeling and simulation of the interactions of a large number of living entities, and provides a presentation of the papers...

CNR@People | DOI: 10.1142/S0218202518020013
2018, Journal article
Lowest order Virtual Element approximation of magnetostatic problems
L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini, and A. Russo
We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use forthe numerical solution of linear magneto-static problems in three dimensions. The met...

CNR@People | DOI: 10.1016/j.cma.2017.12.028
2018, Journal article
Serendipity virtual elements for general elliptic equations in three dimensions
L. Beirao Da Veiga, F. Brezzi, F. Dessi, L.D. Marini, and A. Russo
The authors study the use of the virtual element method (VEM for short) of order k for general second order elliptic problems with variable coefficients in three space dimensions. Moreover, they inves...

CNR@People | DOI: 10.1007/s11401-018-1066-4
2017, Journal article
Mathematical models of self-propelled particles
N. Bellomo and F. Brezzi
This paper presents the papers published in two special issues devoted to the modeling of large systems of self-propelled particles. The contents of these papers are presented in the general framework...

CNR@People | DOI: 10.1142/S021820251702002X
2017, Journal article
Modeling behavioral social systems
N. Bellomo, F. Brezzi, and M. Pulvirenti
This paper presents the papers published in a special issue devoted to the modeling of behavioral social systems. Some perspective ideas on possible objectives of future research are extracted from th...

CNR@People | DOI: 10.1142/S0218202517020018
2017, Journal article
Serendipity face and edge VEM spaces
L. Beirao Da Veiga, F. Brezzi, L.D. Marini, and A. Russo
We extend the basic idea of Serendipity Virtual Elements from the previous case (by the same authors) of nodal (piecewise smooth and continuous) elements, to a more general framework. Then we apply th...

CNR@People | DOI: 10.4171/RLM/756
2017, Journal article
Virtual Element approximation of 2D magnetostatic problems
L. Beirao da Veiga, F. Brezzi, F. Dassi, L.D. Marini, and A. Russo
We consider the use of nodal and edge Virtual Element spaces for the discretization of magnetostatic problems in two dimensions, following the variational formulation of Kikuchi. In addition, we prese...

CNR@People | DOI: 10.1016/j.cma.2017.08.013
2016, Journal article
H(div) and H(curl)-conforming virtual element methods
L. Beirao da Veiga, F. Brezzi, L.D. Marini, and A. Russo
In the present paper we construct virtual element spaces that are (Formula presented.)-conforming and (Formula presented.)-conforming on general polygonal and polyhedral elements; these spaces can be ...

CNR@People | DOI: 10.1007/s00211-015-0746-1
2016, Journal article
Mathematics, complexity and multiscale features of large systems of self-propelled particles
N. Bellomo and F. Brezzi
This issue is devoted to complex systems in life sciences. Some perspective ideas on possible objectives of future research are extracted from the contents of this issue and brought to the reader's at...

CNR@People | DOI: 10.1142/S0218202516020012
2016, Journal article
Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes
L. Beirao da Veiga, F. Brezzi, L.D. Marini, and A. Russo
In the present paper we introduce a Virtual Element Method (VEM) forthe approximate solution of general linear second order elliptic problems in mixed form,allowing for variable coecients. We derive a...

CNR@People | DOI: 10.1051/m2an/2015067
2016, Journal article
Serendipity nodal VEM spaces
L. Beirao da Veiga, F. Brezzi, L.D. Marini, and A. Russo
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 to reduce...

CNR@People | DOI: 10.1016/j.compfluid.2016.02.015
2016, Journal article
Virtual Element Method for general second-order elliptic problems on polygonal meshes
L. Beirao da Veiga, F. Brezzi, L.D. Marini, and A. Russo
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 [A. H. Schatz, An obse...

CNR@People | DOI: 10.1142/S0218202516500160
2015, Journal article
An "immersed" finite element method based on a locally anisotropic remeshing for the incompressible Stokes problem
F. Auricchio, F. Brezzi, A. Lefieux, and A. Reali
In the present paper we study a finite element method for the incompressible Stokes problem with a boundary immersed in the domain on which essential constraints are imposed. Such type of methods may ...

CNR@People | DOI: 10.1016/j.cma.2014.10.001
2015, Journal article
Traffic, crowds, and dynamics of self-organized particles: New trends and challenges
N. Bellomo and F. Brezzi
This brief note is an introduction to the special issue devoted to modeling, qualitative analysis and simulations of vehicular traffic, crowds and swarms, viewed as living, hence complex, systems. The...

CNR@People | DOI: 10.1142/S0218202515020017
2014, Journal article
A simple preconditioner for a Discontinuous Galerkin method for the Stokes problem
B. Ayuso de Dios, F. Brezzi, L.D. Marini, J. Xu, and L. Zikatanov
In this paper we construct Discontinuous Galerkin approximations of the Stokes problem where the velocity field is H(div, ?)-conforming. This implies that the velocity solution is divergence-free in t...

CNR@People | DOI: 10.1007/s10915-013-9758-0
2014, Journal article
Basic principles of mixed virtual element methods
F. Brezzi, R.S. Falk, and L.D. Marini
The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields (or, more generally, of (n-...

CNR@People | DOI: 10.1051/m2an/2013138
2014, Journal article
Complex systems: New challenges with modeling headaches
N. Bellomo and F. Brezzi
This brief note is an introduction to the papers published in this special issue devoted to complex systems in life sciences. Out of this presentation some perspective ideas on conceivable future rese...

CNR@People | DOI: 10.1142/S0218202513020016
2014, Journal article
Mimetic scalar products of discrete differential forms
F. Brezzi, A. Buffa, and G. Manzini
We propose a strategy for the systematic construction of the mimetic inner products on cochain spaces for the numerical approximation of partial differential equations on unstructured polygonal and po...

CNR@People | DOI: 10.1016/j.jcp.2013.08.017
2014, Journal article
The hitchhiker's guide to the virtual element method
L. Beirao da Veiga, F. Brezzi, L.D. Marini, and A. Russo
We present the essential ingredients in the Virtual Element Method for a simple linear elliptic second-order problem. We emphasize its computer implementation, which will enable interested readers to ...

CNR@People | DOI: 10.1142/S021820251440003X
2013, Journal article
Basic principles of virtual element methods
L. Beirao da Veiga, F. Brezzi, C. Cangiani, G. Manzini, L. D. Marini, and A. Russo
We present, on the simplest possible case, what we consider as the very basic features of the (brand new) virtual element method. As the readers will easily recognize, the virtual element method could...

CNR@People | DOI: 10.1142/S0218202512500492
2013, Journal article
Equivalent projectors for virtual element methods
B. Ahmad, A. Alsaedi, F. Brezzi, L.D. Marini, and A. Russo
In the original virtual element space with degree of accuracy kk, projector operators in the H1H1-seminorm onto polynomials of degree <=k<=k can be easily computed. On the other hand, projections in t...

CNR@People | DOI: 10.1016/j.camwa.2013.05.015
2013, Journal article
Virtual Element Methods for plate bending problems
F. Brezzi and L.D. Marini
We discuss the application of Virtual Elements to linear plate bending problems, in the Kirchhoff-Love formulation. As we shall see, in the Virtual Element environment the treatment of the C1C1-cont...

CNR@People | DOI: 10.1016/j.cma.2012.09.012
2013, Journal article
Virtual elements for linear elasticity problems
L. Beirao Da Veiga, F. Brezzi, and L.D. Marini
We discuss the application of virtual elements to linear elasticity problems, for both the compressible and the nearly incompressible case. Virtual elements are very close to mimetic finite difference...

CNR@People | DOI: 10.1137/120874746
2012, Journal article
Analytical modelling of a large-scale dynamic testing facility
P. Ceresa, F. Brezzi, G.M. Calvi, and R. Pinho
An analytical model, which aims at reproducing the response of a large-scale dynamic testing facility, that is a system composed of the specimen/shaking table/reaction-mass/airbags/dampers/soil is dev...

CNR@People | DOI: 10.1002/eqe.1128
2012, Journal article
L2-estimates for the DG IIPG-0 scheme
B. Ayuso de Dios, F. Brezzi, O. Havle, and L.D. Marini
We discuss the optimality in L2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and th...

CNR@People | DOI: 10.1002/num.20687
2011, Journal article
Mathematics and complexity in biological sciences
N. Bellomo and F. Brezzi
This special issue continues the tradition of the journal Mathematical Models andMethods in Applied Sciences on the modeling, qualitative analysis, and simulation ofcomplex systems. More precisely, sy...

CNR@People | DOI: 10.1142/S0218202511005374
2011, Journal article
New rectangular plate elements based on twist-Kirchhoff theory
F. Brezzi, J.A. Evans, T.J.R. Hughes, and L.D. Marini
We introduce a new framework for the development of thin plate finite elements, the "twist-Kirchhoff theory". A family of rectangular plate elements is derived that takes advantage of the sp...

CNR@People | DOI: 10.1016/j.cma.2011.04.012
2011, Journal article
The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes
K. Lipnikov, G. Manzini, F. Brezzi, and A. Buffa
We extend the mimetic finite difference (MFD) method to the numerical treatment of magnetostatic fields problems in mixed div-curl form for the divergence-free magnetic vector potential. To accomplish...

CNR@People | DOI: 10.1016/j.jcp.2010.09.007
2011, Journal article
The MITC9 shell element in plate bending: mathematical analysis of a simplified case
K.-J. Bathe, F. Brezzi, and L.D. Marini
N/A

CNR@People | DOI: 10.1007/s00466-010-0565-2
2010, Journal article
Innovative mimetic discretizations for electromagnetic problems
F. Brezzi and A. Buffa
In this paper we introduce a discretization methodology for Maxwell equations based on Mimetic Finite Differences (MFD). Following the lines of the recent advances in MFD techniques (see Brezzi et al....

CNR@People | DOI: 10.1016/j.cam.2009.08.049
2010, Journal article
Mathematics and complexity in life and human sciences
N. Bellomo, H. Berestycki, F. Brezzi, and J.-P. Nadal
N/A

CNR@People | DOI: 10.1142/S0218202510004702
2009, Journal article
Bubble stabilization of discontinuous Galerkin methods
Antonietti P., Brezzi F., Marini L.D.
N/A

CNR@People
2009, Journal article
Mathematics and complexity in life and human sciences
Bellomo N., Berestycki H., Brezzi F., Nadal J.-P.
N/A

CNR@People
2009, Journal article
Mimetic finite differences for elliptic problems
Brezzi F., Buffa A., Lipnikov K.
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H 1 norm are der...

CNR@People | DOI: 10.1051/m2an:2008046
2009, Journal article
Reduced symmetry elements in linear elasticity
Boffi D., Brezzi F., Fortin M.
N/A

CNR@People
2008, Journal article
Stabilization of the Baumann-Oden DG formulation: the 3D case
Antonietti P., Brezzi F., Marini L.D.
N/A

CNR@People
2008, Journal article
Traffic, crowds, and swarms
Bellomo N., Brezzi F.
N/A

CNR@People
2007, Journal article
A new discretization methodology for diffusion problems on generalized polyhedral meshes
Brezzi F., Lipnikov K., Shashkov M., Simoncini V.
We develop a family of inexpensive discretization schemes for diffusion problems on generalized polyhedral meshes with elements having non-planar faces. The material properties are described by a full...

CNR@People | DOI: 10.1016/j.cma.2006.10.028
2007, Journal article
Locking-free Reissner-Mindlin elements without reduced integration
Arnold D.N., Brezzi F., Falk R.S., Marini L.D.
N/A

CNR@People
2007, Journal article
The method of mothers for non-overlapping non-matching DDM
Bertoluzza S., Brezzi F., Sangalli G.
In this paper we introduce a variant of the three-field formulation where we use only two sets of variables. Considering, to fix the ideas, the Poisson equationwith homogeneous Dirichlet boundary cond...

CNR@People | DOI: 10.1007/s00211-007-0090-1
2006, Journal article
Convergence of mimetic finite difference methods for diffusion problems on polyhedral meshes with curved faces
Brezzi F., Lipnikov K., Shashkov M.
N/A

CNR@People
2006, Journal article
Error analysis of piecewise constant approximations of Darcy's law
Brezzi F., Fortin M., Marini L.D.
N/A

CNR@People
2006, Journal article
Stability and error analysis of mixed finite volume methods for advection dominated problems
Brezzi F.; Marini L.D.; Micheletti S.; Pietra P.; Sacco R.
We consider a convection-diffusion-reaction problem, and we analyze a stabilized mixed finite-volume scheme introduced in S. Micheletti, R. Sacco and F. Saleri (2001). The scheme is presented in the f...

CNR@People | DOI: 10.1016/j.camwa.2006.03.001
2006, Journal article
Stabilization mechanism in Discontinuous Galerkin finite element methods
Brezzi F., Cockburn B., Marini L.D., Süli E.
In this paper we propose a new general framework for the construction and the analysis of discontinuous Galerkin(DG) methods which reveals a basic mechanism, responsible for certain distinctive stabil...

CNR@People | DOI: 10.1016/j.cma.2005.06.015
2005, Journal article
A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate
Arnold D.N., Brezzi F., Marini L.D.
N/A

CNR@People
2005, Journal article
A family of mimetic finite difference methods on polygonal and polyhedral meshes
Brezzi F., Lipnikov K., Simoncini V.
A family of inexpensive discretization schemes for diffusion problems on unstructured polygonal and polyhedral meshes is introduced. The material properties are described by a full tensor. The theoret...

CNR@People | DOI: 10.1142/S0218202505000832
2005, Journal article
Convergence of mimetic finite difference methods for diffusion problems on polyhedral meshes
Brezzi F., Lipnikov K., Shashkov M.
The stability and convergence properties of the mimetic finite difference method fordiffusion-type problems on polyhedral meshes are analyzed. The optimal convergence rates for thescalar and vector va...

CNR@People | DOI: 10.1137/040613950
2005, Journal article
Mixed discontinuous Galerkin methods for Darcy flow
Brezzi F., Hughes T.J.R., Marini L.D., Masud A.
We consider a family of mixed finite element discretizations of the Darcy flow equations using totally discontinuous elements ( both for the pressure and the flux variable). Instead of using a jump st...

CNR@People | DOI: 10.1007/s10915-004-4150-8
2005, Journal article
On the choice of a stabilizing subgrid for convection-diffusion problems
Brezzi F., Marini L.D., Russo A.
N/A

CNR@People
2005, Journal article
The three-field formulation for elasticity problems
Brezzi F., Marini L.D.
N/A

CNR@People
2004, Journal article
Discontinuous Galerkin methods for first-order hyperbolic problems
Brezzi F., Marini L.D., Süli E.
The main aim of this paper is to highlight that, when dealing with DG methods for linearhyperbolic equations or advection-dominated equations, it is much more convenient towrite the upwind numerical u...

CNR@People | DOI: 10.1142/S0218202504003866
2004, Journal article
Reissner-Mindlin plates with free boundary conditions
Beirao da Veiga L., Brezzi F.
N/A

CNR@People
2013, Book
Mixed finite element methos and applications
D. Boffi, F. Brezzi, and M. Fortin
PREFACE. About 10 years ago, Mixed and Hybrid Finite Element Methods by F. Brezzi andM. Fortin went out of print and we were asked to allow a second printing. The worldhad evolved and we thought that ...

CNR@People | Link
2016, Essay or book chapter
Numerical studies on the stability of mixed finite elements over anisotropic meshes arising from immersed boundary Stokes problems
F. Auricchio, F. Brezzi, A. Lefieux, and A. Reali
Motivated by a recently proposed local refinement strategy for immersed interface problems,in this work we aim at dealing with the behavior of mixed finite elements for the Stokes problem in (strongly...

CNR@People | DOI: 10.1007/978-3-319-40827-9_25
2016, Preface/Introduction/Postface
Preface
G.R. Barrenechea, F. Brezzi, A. Cangiani, and E.H. Georgoulis
This volume contains survey articles from the topics of a number of the plenarytalks of the 101st LMS-EPSRC Symposium entitled Building Bridges: Connectionsand Challenges in Modern Approaches to Numer...

CNR@People | DOI: 10.1007/978-3-319-41640-3
2016, Essay or book chapter
Virtual element implementation for general elliptic equations
L. Beirao da Veiga, F. Brezzi, L.D. Marini, and A. Russo
In the present paper we detail the implementation of the Virtual Element Method for two dimensional elliptic equations in primal and mixed form with variable coefficients.

CNR@People | DOI: 10.1007/978-3-319-41640-3_2
2014, Essay or book chapter
A Quick Tutorial on DG Methods for Elliptic Problems
F. Brezzi and L.D. Marini
In this paper we recall a few basic definitions and results concerning the use of DG methods for elliptic problems. As examples we consider the Poisson problem and the linear elasticity problem. A hin...

CNR@People | DOI: 10.1007/978-3-319-01818-8_1
2014, Preface/Introduction/Postface
Recent techniques for PDE discretizations on polyhedral meshes
N. Bellomo, F. Brezzi, and G. Manzini
This brief paper is an introduction to the papers published in a special issue devoted to survey on recent techniques for discretizing Partial Differential Equations on general polygonal and polyhedra...

CNR@People | DOI: 10.1142/S0218202514030018
2014, Essay or book chapter
Virtual Element and Discontinuous Galerkin Methods
F. Brezzi and L.D. Marini
Virtual element methods (VEM) are the latest evolution of the MimeticFinite Difference Method and can be considered to be more close to the Finite Elementapproach. They combine the ductility of mimeti...

CNR@People | DOI: 10.1007/978-3-319-01818-8 9
2008, Essay or book chapter
Finite elements for the Stokes problem
Boffi D., Brezzi F., Fortin M.
N/A

CNR@People
2005, Essay or book chapter
Discretization of Semiconductor Device Problems (I)
Brezzi F.;Marini L.D.;Micheletti S.;Pietra P.;Sacco R.; Wang S.
N/A

CNR@People | DOI: 10.1016/S1570-8659(04)13004-4
2004, Essay or book chapter
Mixed finite element methods
Auricchio F., Brezzi F., Lovadina C.
N/A

CNR@People
2004, Essay or book chapter
Piecewise constant pressure for Darcy law
Brezzi F., Fortin M., Marini L.D.
N/A

CNR@People
2015, Conference proceedings
The great beauty of VEM
F. Brezzi
In this paper I review the main features of the (newborn) Virtual Element Method, and ofits application to the approximation of boundary value problems for Partial Differential Equations ofparticular ...

CNR@People | Link
2005, Conference proceedings
Non-matching grids and Lagrange multipliers
S. Bertoluzza, F. Brezzi, L.D. Marini, and G. Sangalli
In this paper we introduce a variant of the three-field formulation where we use only two sets of variables. Considering, to fix the ideas, the homogeneous Dirichlet problem for -Delta u = g in Omega,...

CNR@People | DOI: 10.1007/3-540-26825-1_1
2002, Conference proceedings
Reissner-Mindlin plates with free boundary conditions
Beirao da Veiga L., Brezzi F.
N/A

CNR@People
2016, Curatorship of conference proceedings
Building bridges: Connections and challenges in modern approaches to numerical partial differential equations
G.R.Barrenechea, F. Brezzi, A. Cangiani, and E.H. Georgoulis (Eds.)
This volume contains survey articles from the topics of a number of the plenary talks of the 101st LMS-EPSRC Symposium entitled Building Bridges: Connections and Challenges in Modern Approaches to Num...

CNR@People | DOI: 10.1007/978-3-319-41640-3
2014, Curatorship of journal issues
Special Issue on Recent Techniques for PDE Discretizations on Polyhedral Meshes
N. Bellomo, F. Brezzi, and G. Manzini
This brief paper is an introduction to the papers published in a special issue devoted to survey on recent techniques for discretizing Partial Differential Equations on general polygonal and polyhedra...

CNR@People | Link
2013, Curatorship of books
Analysis and Numerics of Partial Differential Equations
F. Brezzi, P. Colli Franzone, U. Gianazza, and G. Gilardi
On November 2nd 2010 Enrico Magenes passed away.One year later, some of his friends, collaborators and former students organizeda three-day conference, in order to celebrate his memory and give a firs...

CNR@People | DOI: 10.1007/978-88-470-2592-9
2004, Curatorship of books
Reissner-Mindlin plates with free boundary conditions
Beirao da Veiga L., Brezzi F.
N/A

CNR@People