Franco Brezzi

IMATI | Research Associate | Sep 2020

CNR

Publications

Journal Publications

2020, Journal article
Active particles methods and challenges in behavioral systems
N. Bellomo, F. Brezzi, and J. Soler
Mathematical models and methods in applied sciences 30(4) pp. 653-658
CNR@IRIS | DOI: 10.1142/S0218202520020017

2019, Journal article
Towards a multiscale vision of active particles
N. Bellomo and F. Brezzi
Mathematical models and methods in applied sciences 29(4) pp. 581-588
CNR@IRIS | 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
SIAM journal on numerical analysis 56(5) pp. 2940-2962
CNR@IRIS | DOI: 10.1137/18M1169886

2018, Journal article
Challenges in active particles methods: Theory and applications
N. Bellomo and F. Brezzi
Mathematical models and methods in applied sciences 28(9) pp. 1627-1633
CNR@IRIS | 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
Computer methods in applied mechanics and engineering 332 pp. 343-362
CNR@IRIS | 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
Chinese annals of mathematics. Ser. B 39(2) pp. 315-334
CNR@IRIS | DOI: 10.1007/s11401-018-1066-4

2017, Journal article
Mathematical models of self-propelled particles
N. Bellomo and F. Brezzi
Mathematical models and methods in applied sciences 27(6) pp. 1-8
CNR@IRIS | DOI: 10.1142/S021820251702002X

2017, Journal article
Modeling behavioral social systems
N. Bellomo, F. Brezzi, and M. Pulvirenti
Mathematical models and methods in applied sciences 27(1) pp. 1-11
CNR@IRIS | 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
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni (Testo stamp.) 28(1) pp. 143-180
CNR@IRIS | 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
Computer methods in applied mechanics and engineering 327 pp. 173-195
CNR@IRIS | 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
Numerische Mathematik 133(2) pp. 303-332
CNR@IRIS | 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
Mathematical models and methods in applied sciences 26(2) pp. 207-214
CNR@IRIS | 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
Modélisation mathématique et analyse numérique (Impr.) 50(3) pp. 727-747
CNR@IRIS | DOI: 10.1051/m2an/2015067

2016, Journal article
Serendipity nodal VEM spaces
L. Beirao da Veiga, F. Brezzi, L.D. Marini, and A. Russo
Computers & fluids 141 pp. 2-12
CNR@IRIS | 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
Mathematical models and methods in applied sciences 26(4) pp. 729-750
CNR@IRIS | 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
Computer methods in applied mechanics and engineering 294 pp. 428-448
CNR@IRIS | 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
Mathematical models and methods in applied sciences 25(3) pp. 395-400
CNR@IRIS | 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
Journal of scientific computing 58(3) pp. 517-547
CNR@IRIS | 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
Modélisation mathématique et analyse numérique (En ligne) 48(4) pp. 1227-1240
CNR@IRIS | DOI: 10.1051/m2an/2013138

2014, Journal article
Complex systems: New challenges with modeling headaches
N. Bellomo and F. Brezzi
Mathematical models and methods in applied sciences 24(2) pp. 213-219
CNR@IRIS | DOI: 10.1142/S0218202513020016

2014, Journal article
Mimetic scalar products of discrete differential forms
F. Brezzi, A. Buffa, and G. Manzini
Journal of computational physics 257 pp. 1228-1259
CNR@IRIS | 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
Mathematical models and methods in applied sciences 24(8) pp. 1541-1573
CNR@IRIS | 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
Mathematical models and methods in applied sciences 23(1) pp. 199-214
CNR@IRIS | 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
Computers & mathematics with applications (1987) 66(3) pp. 376-391
CNR@IRIS | DOI: 10.1016/j.camwa.2013.05.015

2013, Journal article
Virtual Element Methods for plate bending problems
F. Brezzi and L.D. Marini
Computer methods in applied mechanics and engineering 253 pp. 455-462
CNR@IRIS | 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
SIAM journal on numerical analysis 51(2) pp. 794-812
CNR@IRIS | 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
Earthquake engineering & structural dynamics 41(2) pp. 255-277
CNR@IRIS | 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
Numerical methods for partial differential equations 28(5) pp. 1440-1465
CNR@IRIS | DOI: 10.1002/num.20687

2011, Journal article
Mathematics and complexity in biological sciences
N. Bellomo and F. Brezzi
Mathematical models and methods in applied sciences 20 pp. 819-824
CNR@IRIS | 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
Computer methods in applied mechanics and engineering 200 pp. 2547-2561
CNR@IRIS | 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
Journal of computational physics 230 pp. 305-328
CNR@IRIS | 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
Computational mechanics 47 pp. 617-6126
CNR@IRIS | DOI: 10.1007/s00466-010-0565-2

2010, Journal article
Innovative mimetic discretizations for electromagnetic problems
F. Brezzi and A. Buffa
Journal of computational and applied mathematics 234 pp. 1980-1987
CNR@IRIS | 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
Mathematical models and methods in applied sciences 20(suppl) pp. 1391-1395
CNR@IRIS | DOI: 10.1142/S0218202510004702

2009, Journal article
Bubble stabilization of discontinuous Galerkin methods
Antonietti P., Brezzi F., Marini L.D.
Computer methods in applied mechanics and engineering 198 pp. 1651-1659
CNR@IRIS

2009, Journal article
Mathematics and complexity in life and human sciences
Bellomo N., Berestycki H., Brezzi F., Nadal J.-P.
Mathematical models and methods in applied sciences 19 pp. 1385-1389
CNR@IRIS

2009, Journal article
Mimetic finite differences for elliptic problems
Brezzi F., Buffa A., Lipnikov K.
Modélisation mathématique et analyse numérique (Impr.) 43 pp. 277-295
CNR@IRIS | DOI: 10.1051/m2an:2008046

2009, Journal article
Reduced symmetry elements in linear elasticity
Boffi D., Brezzi F., Fortin M.
Communications on pure and applied analysis 8 pp. 95-121
CNR@IRIS

2008, Journal article
Stabilization of the Baumann-Oden DG formulation: the 3D case
Antonietti P., Brezzi F., Marini L.D.
Bollettino della Unione matematica italiana (1922) 1 pp. 629-643
CNR@IRIS

2008, Journal article
Traffic, crowds, and swarms
Bellomo N., Brezzi F.
Mathematical models and methods in applied sciences 18 pp. 1145-1148
CNR@IRIS

2007, Journal article
A new discretization methodology for diffusion problems on generalized polyhedral meshes
Brezzi F., Lipnikov K., Shashkov M., Simoncini V.
Computer methods in applied mechanics and engineering 196(37-40) pp. 3682-3692
CNR@IRIS | 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.
Computer methods in applied mechanics and engineering 196 pp. 3660-3671
CNR@IRIS

2007, Journal article
The method of mothers for non-overlapping non-matching DDM
Bertoluzza S., Brezzi F., Sangalli G.
Numerische Mathematik 107 pp. 397-431
CNR@IRIS | 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.
Mathematical models and methods in applied sciences 16 pp. 275-298
CNR@IRIS

2006, Journal article
Error analysis of piecewise constant approximations of Darcy's law
Brezzi F., Fortin M., Marini L.D.
Computer methods in applied mechanics and engineering 195 pp. 1547-1599
CNR@IRIS

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.
Computers & mathematics with applications (1987) 51(5) pp. 681-696
CNR@IRIS | 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.
Computer methods in applied mechanics and engineering 195(25-28) pp. 3293-3310
CNR@IRIS | 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.
Journal of scientific computing 22 pp. 25-45
CNR@IRIS

2005, Journal article
A family of mimetic finite difference methods on polygonal and polyhedral meshes
Brezzi F., Lipnikov K., Simoncini V.
Mathematical models and methods in applied sciences 15(10) pp. 1533-1551
CNR@IRIS | 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.
SIAM journal on numerical analysis 43(5) pp. 1872-1896
CNR@IRIS | 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.
Journal of scientific computing 22(1) pp. 119-145
CNR@IRIS | 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.
Computer methods in applied mechanics and engineering 194 pp. 127-148
CNR@IRIS

2005, Journal article
The three-field formulation for elasticity problems
Brezzi F., Marini L.D.
28 pp. 124-153
CNR@IRIS

2004, Journal article
Discontinuous Galerkin methods for first-order hyperbolic problems
Brezzi F., Marini L.D., Süli E.
Mathematical models and methods in applied sciences 14(12) pp. 1893-1903
CNR@IRIS | DOI: 10.1142/S0218202504003866

2004, Journal article
Reissner-Mindlin plates with free boundary conditions
Beirao da Veiga L., Brezzi F.
210 pp. 43-54
CNR@IRIS

Part of book

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
Advances in Computational Fluid-Structure Interaction and Flow Simulation: New Methods and Challenging Computations pp. 319-330 (Modeling and simulation in science, engineering & technology ), edited by Bazilevs Yuri, Takizawa Kenij. Springer International Publishing, 978-3-319-40825-5
CNR@IRIS | 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
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations pp. v-vi (Lecture notes in computational science and engineering), edited by Barrenechea G., Brezzi F., Cangiani A., Georgoulis E.H.. Springer International Publishing, 978-3-319-41638-0
CNR@IRIS | 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
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations pp. 39-71, edited by Barrenechea G.R., Brezzi F., Cangiani A.,Georgoulis E.H.. Springer International Publishing, 978-3-319-41638-0
CNR@IRIS | 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
Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations pp. 1-24 (The IMA volumes in mathematics and its applications), edited by X. Feng et al.. Springer International Publishing, 978-3-319-01817-1
CNR@IRIS | 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
Special Issue on Recent Techniques for PDE Discretizations on Polyhedral Meshes pp. 1453-1455 World Scientific Publ. Co.
CNR@IRIS | DOI: 10.1142/S0218202514030018

2014, Essay or book chapter
Virtual Element and Discontinuous Galerkin Methods
F. Brezzi and L.D. Marini
Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations pp. 209-221 (The IMA volumes in mathematics and its applications), edited by X. Feng et al.. Springer International Publishing, 978-3-319-01817-1
CNR@IRIS | 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.
Springer-Verlag
CNR@IRIS

2005, Essay or book chapter
Discretization of Semiconductor Device Problems (I)
Brezzi F.;Marini L.D.;Micheletti S.;Pietra P.;Sacco R.; Wang S.
Numerical Methods in Electromagnetics pp. 317-441 (Handbook of numerical analysis ), edited by Schilders W.H.A.;Maten E.J.W.. North Holland Pub. Co., 0-444-51375-2
CNR@IRIS | DOI: 10.1016/S1570-8659(04)13004-4

2004, Essay or book chapter
Mixed finite element methods
Auricchio F., Brezzi F., Lovadina C.
John Wiley & Sons Ltd.
CNR@IRIS

2004, Essay or book chapter
Piecewise constant pressure for Darcy law
Brezzi F., Fortin M., Marini L.D.

CNR@IRIS

Book

2021, Curatorship of journal issues
Calcolo: A Quarterly on Numerical Analysis and Theory of Computation Vol 58
F. Brezzi (1); D. Bini (2); N. Guglielmi (3); M. Benzi (4); P. Favati (5)
p. (Calcolo (Testo stamp.))
CNR@IRIS

2014, Curatorship of journal issues
Special Issue on Recent Techniques for PDE Discretizations on Polyhedral Meshes
N. Bellomo, F. Brezzi, and G. Manzini
274
CNR@IRIS | Link

2013, Curatorship of books
Analysis and Numerics of Partial Differential Equations
F. Brezzi, P. Colli Franzone, U. Gianazza, and G. Gilardi
366 p. (Springer INdAM Series), 978-88-470-2591-2
CNR@IRIS | DOI: 10.1007/978-88-470-2592-9

2013, Book
Mixed finite element methos and applications
D. Boffi, F. Brezzi, and M. Fortin
685 p. (Springer series in computational mathematics), 978-3-642-36518-8
CNR@IRIS | Link

2004, Curatorship of books
Reissner-Mindlin plates with free boundary conditions
Beirao da Veiga L., Brezzi F.

CNR@IRIS

Conference proceedings

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.)
pp. 1-431, Springer International Publishing, 978-3-319-41638-0
CNR@IRIS | DOI: 10.1007/978-3-319-41640-3

2015, Conference proceedings
The great beauty of VEM
F. Brezzi
Proceedings of the International Congress of Mathematicians, Seoul 2014 pp. 217-235, edited by Sun Young Jan et al.. (International Congress of Mathematicians, Seoul, Korea, 13-21/08/2014), 978-89-6105-804-9
CNR@IRIS | Link

2005, Conference proceedings
Non-matching grids and Lagrange multipliers
S. Bertoluzza, F. Brezzi, L.D. Marini, and G. Sangalli
Domain Decomposition Methods in Science and Engineering pp. 3-18 (Lecture notes in computational science and engineering), edited by Timothy J. Barth, Michael Griebel, David E. Keyes, Risto M. Nieminen, Dirk Roose,Tamar Schlick, Ralf Kornhuber, Ronald Hoppe, Jacques Périaux, Olivier Pironneau, Olof Widlund, Jinchao Xu., Springer (15th International Conference on Domain Decomposition, Berlino, 25-28/07/2003), 978-3-540-22523-2
CNR@IRIS | DOI: 10.1007/3-540-26825-1_1

2002, Conference proceedings
Reissner-Mindlin plates with free boundary conditions
Beirao da Veiga L., Brezzi F.
(Whence the boundary conditions in modern continuum physics?, Roma)
CNR@IRIS

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