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A Virtual Element Method for the Steklov Eigenvalue Problem Allowing Small Edges

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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.

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Acknowledgements

FL was partially supported by the National Agency for Research and Development, ANID-Chile through FONDECYT Postdoctorado project 3190204 and FONDECYT project 11200529. DM was partially supported by the National Agency for Research and Development, ANID-Chile through FONDECYT project 1180913 and by project AFB170001 of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal. GR was partially supported by the National Agency for Research and Development, ANID-Chile through FONDECYT project 11170534. IV was partially supported by project AFB170001 of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile

    Felipe Lepe & David Mora

  2. CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    David Mora & Iván Velásquez

  3. Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile

    Gonzalo Rivera

  4. Departamento de Ciencias Básicas, Universidad del Sinú-Elías Bechara Zainúm, Montería, Colombia

    Iván Velásquez

  5. GIMNAP-Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile

    Felipe Lepe & David Mora

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  1. Felipe Lepe
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  2. David Mora
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  4. Iván Velásquez
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Correspondence to Gonzalo Rivera.

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Lepe, F., Mora, D., Rivera, G. et al. A Virtual Element Method for the Steklov Eigenvalue Problem Allowing Small Edges. J Sci Comput 88, 44 (2021). https://doi.org/10.1007/s10915-021-01555-3

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