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A virtual element method for the elasticity problem allowing small edges

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Abstract

In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In particular, we consider only star-shaped polygons for the meshes. Suitable error estimates are presented, where a rigorous analysis on the influence of the Lamé constants in each estimate is presented. We report numerical tests to assess the performance of the method.

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Acknowledgements

D. Amigo and F. Lepe were partially supported by DIUBB through project 2120173 GI/C Universidad del Bío-Bío and ANID-Chile through FONDECYT project 11200529 (Chile). G. Rivera was partially supported by Universidad de Los Lagos through regular project R02/21.

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Authors and Affiliations

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

    Danilo Amigo & Felipe Lepe

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

    Gonzalo Rivera

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  1. Danilo Amigo
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  2. Felipe Lepe
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  3. Gonzalo Rivera
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Correspondence to Felipe Lepe.

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Amigo, D., Lepe, F. & Rivera, G. A virtual element method for the elasticity problem allowing small edges. Calcolo 60, 28 (2023). https://doi.org/10.1007/s10092-023-00522-8

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  • DOI: https://doi.org/10.1007/s10092-023-00522-8

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