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A virtual element method for the Steklov eigenvalue problem allowing small edges (2006.09573v1)
Published 17 Jun 2020 in math.NA and cs.NA
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.