The nonconforming virtual element method

Ayuso de Dios, Blanca; Lipnikov, Konstantin; Manzini, Gianmarco

doi:10.1051/m2an/2015090

Ayuso de Dios, Blanca ^1,² ; Lipnikov, Konstantin ³ ; Manzini, Gianmarco ^2,³

¹ Institut für Mathematik, Technische Universität Hamburg-Harburg, Am Schwarzenberg-Campus 3, D-21073 Hamburg, Germany
² Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) – CNR, 27100 Pavia, Italy
³ Applied Mathematics and Plasma Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 879-904.

Résumé

We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method.

Reçu le : 2015-04-26

MR Zbl | 7 citations dans Numdam

DOI : 10.1051/m2an/2015090

Classification : 65N30, 65N12, 65G99, 76R99
Mots-clés : Virtual element method, nonconforming method, Poisson equation, elliptic problems, unstructured meshes

Affiliations des auteurs :

Ayuso de Dios, Blanca ^{1, 2} ; Lipnikov, Konstantin ³ ; Manzini, Gianmarco ^{2, 3}

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     title = {The nonconforming virtual element method},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {879--904},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {3},
     year = {2016},
     doi = {10.1051/m2an/2015090},
     mrnumber = {3507277},
     zbl = {1343.65140},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2015090/}
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Ayuso de Dios, Blanca; Lipnikov, Konstantin; Manzini, Gianmarco. The nonconforming virtual element method. ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 879-904. doi : 10.1051/m2an/2015090. http://www.numdam.org/articles/10.1051/m2an/2015090/

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