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Challenges and Advancements in Virtual Elements

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Publications

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
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
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
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
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
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
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
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
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
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
DOI: 10.1007/s00211-019-01054-6