Felipe Lepe, David Mora, Gonzalo Rivera, Iván Velásquez:
A virtual element method for the Steklov eigenvalue problem allowing small edges
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.
This preprint gave rise to the following definitive publication(s):
Felipe LEPE, David MORA, Gonzalo RIVERA, Iván VELáSQUEZ: A virtual element method for the Steklov eigenvalue problem allowing small edges. Journal of Scientific Computing, vol. 82, 2, Art. Num. 44, (2021).