Geodesic
The nonconforming Virtual Element Method for eigenvalue problems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 3, pp. 749-774.

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We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allows to treat in the same formulation the two- and three-dimensional case. We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problem. The proposed schemes provide a correct approximation of the spectrum, in particular we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

DOI : 10.1051/m2an/2018074
Classification : 65N30, 65N25
Keywords: Nonconforming virtual element, eigenvalue problem, polygonal meshes

Gardini, Francesca 1 ; Manzini, Gianmarco 1 ; Vacca, Giuseppe 1

1 
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Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe. The nonconforming Virtual Element Method for eigenvalue problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 3, pp. 749-774. doi : 10.1051/m2an/2018074. http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018074/

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