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Pre-Publicación 2020-15

Felipe Lepe, David Mora, Gonzalo Rivera, Iván Velásquez:

A virtual element method for the Steklov eigenvalue problem allowing small edges

Abstract:

The aim of this paper is to analyze the influence of small edges in the computation of the spectrum of the Steklov eigenvalue problem by a lowest order virtual element method. Under weaker assumptions on the polygonal meshes, which can permit arbitrarily small edges with respect to the element diameter, we show that the scheme provides a correct approximation of the spectrum and prove optimal error estimates for the eigenfunctions and a double order for the eigenvalues. Finally, we report some numerical tests supporting the theoretical results.

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