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Challenges and Advancements in Virtual Elements

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Publications

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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 375, 2021, Page(s) 113649, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/j.cma.2020.113649