Challenges and Advancements in Virtual Elements

Project Information

CAVE

Grant agreement ID: 681162

DOI

10.3030/681162

Project closed

EC signature date 3 March 2016

Start date 1 July 2016

End date 30 June 2021

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 980 634,00

EU contribution

€ 980 634,00

Coordinated by

UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA
Italy

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (20)

A C 1 Virtual Element Method on polyhedral meshes

Author(s): L. Beirão da Veiga, F. Dassi, A. Russo
Published in: Computers & Mathematics with Applications, Issue 79/7, 2020, Page(s) 1936-1955, ISSN 0898-1221
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.camwa.2019.06.019

Polynomial preserving virtual elements with curved edges

Author(s): L. Beirão da Veiga, F. Brezzi, L. D. Marini, A. Russo
Published in: Mathematical Models and Methods in Applied Sciences, Issue 30/08, 2020, Page(s) 1555-1590, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202520500311

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

Author(s): F. Dassi, S. Scacchi
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 372, 2020, Page(s) 113424, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2020.113424

The Stokes Complex for Virtual Elements with Application to Navier–Stokes Flows

Author(s): L. Beirão da Veiga, D. Mora, G. Vacca
Published in: Journal of Scientific Computing, Issue 81/2, 2019, Page(s) 990-1018, ISSN 0885-7474
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-01049-3

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

Author(s): L. Beirão da Veiga, C. Canuto, R. H. Nochetto, G. Vacca
Published in: Mathematical Models and Methods in Applied Sciences, 2021, Page(s) 1-50, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202521500275

Curvilinear virtual elements for contact mechanics

Author(s): Fadi Aldakheel, Blaž Hudobivnik, Edoardo Artioli, Lourenço Beirão da Veiga, Peter Wriggers
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 372, 2020, Page(s) 113394, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2020.113394

An adaptive curved virtual element method for the statistical homogenization of random fibre-reinforced composites

Author(s): E. Artioli, L. Beirão da Veiga, M. Verani
Published in: Finite Elements in Analysis and Design, Issue 177, 2020, Page(s) 103418, ISSN 0168-874X
Publisher: Elsevier BV
DOI: 10.1016/j.finel.2020.103418

Stability analysis for the virtual element method

Author(s): Lourenço Beirão da Veiga, Carlo Lovadina, Alessandro Russo
Published in: Mathematical Models and Methods in Applied Sciences, Issue 27/13, 2017, Page(s) 2557-2594, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/S021820251750052X

High-order Virtual Element Method on polyhedral meshes

Author(s): L. Beirão da Veiga, F. Dassi, A. Russo
Published in: Computers & Mathematics with Applications, Issue 74/5, 2017, Page(s) 1110-1122, ISSN 0898-1221
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.camwa.2017.03.021

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

Author(s): H. Chi, L. Beirão da Veiga, G.H. Paulino
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 318, 2017, Page(s) 148-192, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2016.12.020

Virtual Element approximation of 2D magnetostatic problems

Author(s): L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini, A. Russo
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 327, 2017, Page(s) 173-195, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2017.08.013

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

Author(s): L. Beirão da Veiga, A. Chernov, L. Mascotto, A. Russo
Published in: Numerische Mathematik, Issue 138, 2017, Page(s) 581–613, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-017-0921-7

Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes

Author(s): L. Beira͂o da Veiga, C. Lovadina, G. Vacca
Published in: SIAM Journal on Numerical Analysis, Issue 56/3, 2018, Page(s) 1210-1242, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/17m1132811

The Virtual Element Method with curved edges

Author(s): Lourenço Beirão da Veiga, Alessandro Russo, Giuseppe Vacca
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, 2019, ISSN 0764-583X
Publisher: EDP Sciences
DOI: 10.1051/m2an/2018052

Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems

Author(s): Lourenço Beirão da Veiga, Franco Brezzi, L. Donatella Marini, Alessandro Russo
Published in: SMAI Journal of Computational Mathematics, Issue 4, 2018, Page(s) 399-416, ISSN 2426-8399
Publisher: SMAI
DOI: 10.5802/smai-jcm.40

Lowest order Virtual Element approximation of magnetostatic problems

Author(s): L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini, A. Russo
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 332, 2018, Page(s) 343-362, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2017.12.028

A posteriori error estimation and adaptivity in hp virtual elements

Author(s): L. Beirao da Veiga, G. Manzini, L. Mascotto
Published in: Numerische Mathematik, 2019, ISSN 0945-3245
Publisher: Springer Verlag
DOI: 10.1007/s00211-019-01054-6

The Stokes complex for Virtual Elements in three dimensions

Author(s): L. Beirão da Veiga, F. Dassi, G. Vacca
Published in: Mathematical Models and Methods in Applied Sciences, Issue 30/03, 2020, Page(s) 477-512, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202520500128

Curvilinear Virtual Elements for 2D solid mechanics applications

Author(s): E. Artioli, L. Beirão da Veiga, F. Dassi
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 359, 2020, Page(s) 112667, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2019.112667

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

Author(s): L. Beirão da Veiga, A. Pichler, G. Vacca
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 375, 2021, Page(s) 113649, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2020.113649