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DOE OSTI · 1844151

The nonconforming Virtual Element Method for eigenvalue problems

Gardini, Francesca·Manzini, Gianmarco·Vacca, Giuseppe
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Abstract

In this work, 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 $L^2$-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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97 MATHEMATICS AND COMPUTINGmathematicsnonconforming virtual element, eigenvalue problem, polygonal mesh

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Gardini, Francesca, Manzini, Gianmarco, Vacca, Giuseppe. 2019-06-05. The nonconforming Virtual Element Method for eigenvalue problems. https://doi.org/10.1051/m2an%2F2018074

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