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.
Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(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).