Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 88, Issue 2, Pages -Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-021-01555-3
Keywords
Virtual element method; Steklov eigenvalue problem; Error estimates; Polygonal meshes; Small edges
Categories
Funding
- National Agency for Research and Development, ANID-Chile through FONDECYT Postdoctorado project [3190204]
- FONDECYT project [11200529]
- National Agency for Research and Development, ANID-Chile through FONDECYT project [1180913, 11170534]
- PIA Program: Concurso Apoyo a Centros Cientificos y Tecnologicos de Excelencia con Financiamiento Basal [AFB170001]
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This paper analyzes the influence of small edges in the computation of the spectrum of the Steklov eigenvalue problem using a lowest order virtual element method. The scheme is shown to provide a correct approximation of the spectrum under weaker assumptions on the polygonal meshes. Optimal error estimates for eigenfunctions and double order for eigenvalues are proven, with numerical tests supporting the theoretical results.
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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