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A Posteriori Analysis for a Mixed FEM Discretization of the Linear Elasticity Spectral Problem

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Abstract

In this paper we analyze a posteriori error estimates for a mixed formulation of the linear elasticity eigenvalue problem. A posteriori estimators for the nearly and perfectly compressible elasticity spectral problems are proposed. With a post-process argument, we are able to prove reliability and efficiency for the proposed estimators. The numerical method is based in Raviart-Thomas elements to approximate the pseudostress and piecewise polynomials for the displacement. We illustrate our results with numerical tests in two and three dimensions.

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Funding

The first author was partially supported by DIUBB through project 2120173 GI/C Universidad del Bío-Bío and ANID-Chile through FONDECYT project 11200529 (Chile). The third author author was partially supported by ANID-Chile through project Anillo of Computational Mathematics for Desalination Processes ACT210087.

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Authors and Affiliations

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

    Felipe Lepe & Jesus Vellojin

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

    Gonzalo Rivera

Authors
  1. Felipe Lepe
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  2. Gonzalo Rivera
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  3. Jesus Vellojin
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Correspondence to Gonzalo Rivera.

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Lepe, F., Rivera, G. & Vellojin, J. A Posteriori Analysis for a Mixed FEM Discretization of the Linear Elasticity Spectral Problem. J Sci Comput 93, 10 (2022). https://doi.org/10.1007/s10915-022-01972-y

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  • DOI: https://doi.org/10.1007/s10915-022-01972-y

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