A virtual element method for the Steklov eigenvalue problem allowing small edges
Numerical Analysis
2020-06-18 v1 Numerical Analysis
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.
Cite
@article{arxiv.2006.09573,
title = {A virtual element method for the Steklov eigenvalue problem allowing small edges},
author = {Felipe Lepe and David Mora and Gonzalo Rivera and Iván Velásquez},
journal= {arXiv preprint arXiv:2006.09573},
year = {2020}
}