Mixed virtual element methods for general second order elliptic problems on polygonal meshes

Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, Luisa Donatella; Russo, Alessandro

doi:10.1051/m2an/2015067

Beirão da Veiga, Lourenço ^1,² ; Brezzi, Franco ² ; Marini, Luisa Donatella ^2,³ ; Russo, Alessandro ^1,²

¹ Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Cozzi 57, 20125 Milano, Italy
² IMATI del CNR, Via Ferrata 1, 27100 Pavia, Italy
³ Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy

ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 727-747.

Résumé

In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis of the method and develop a set of numerical tests on a benchmark problem with known solution.

Reçu le : 2015-04-12

MR Zbl | 4 citations dans Numdam

DOI : 10.1051/m2an/2015067

Classification : 65N30
Mots-clés : Mixed Virtual Element Methods, elliptic problems

Affiliations des auteurs :

Beirão da Veiga, Lourenço ^{1, 2} ; Brezzi, Franco ² ; Marini, Luisa Donatella ^{2, 3} ; Russo, Alessandro ^{1, 2}

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     title = {Mixed virtual element methods for general second order elliptic problems on polygonal meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {727--747},
     publisher = {EDP-Sciences},
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Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, Luisa Donatella; Russo, Alessandro. Mixed virtual element methods for general second order elliptic problems on polygonal meshes. ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 727-747. doi : 10.1051/m2an/2015067. http://www.numdam.org/articles/10.1051/m2an/2015067/

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