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arXiv · 1802.02942

The nonconforming virtual element method for eigenvalue problems

Francesca Gardini·Gianmarco Manzini·Giuseppe Vacca
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Abstract

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow 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 L^2-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.

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Francesca Gardini, Gianmarco Manzini, Giuseppe Vacca. 2018-02-08. The nonconforming virtual element method for eigenvalue problems. https://arxiv.org/abs/1802.02942

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