Geodesic
Mixed virtual element methods for general second order elliptic problems on polygonal meshes
Beirão da Veiga, Lourenço1, 2  ; Brezzi, Franco2  ; Marini, Luisa Donatella2, 3 ; Russo, Alessandro1, 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

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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 :
DOI : 10.1051/m2an/2015067
Classification : 65N30
Keywords: Mixed Virtual Element Methods, elliptic problems

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 
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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},
     volume = {50},
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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

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