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Equilibrated Stress Reconstructions for Linear Elasticity Problems with Application to a Posteriori Error Analysis

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Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects (FVCA 2017)

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Abstract

We present an a posteriori error estimate for the linear elasticity problem. The estimate is based on an equilibrated reconstruction of the Cauchy stress tensor, which is obtained from mixed finite element solutions of local Neumann problems. We propose two different reconstructions: one using Arnold–Winther mixed finite element spaces providing a symmetric stress tensor, and one using Arnold–Falk–Winther mixed finite element spaces with a weak symmetry constraint. The performance of the estimate is illustrated on a numerical test with analytical solution.

The work of D. A. Di Pietro was supported by ANR grant HHOMM (ANR-15-CE40-0005)

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Authors and Affiliations

  1. IMAG, University of Montpellier, Place Eugène Bataillon, 34090, Montpellier, France

    Rita Riedlbeck & Daniele A. Di Pietro

  2. EDF, R&D, IMSIA, 7, Boulevard Gaspard Monge, 91120, Palaiseau, France

    Rita Riedlbeck

  3. Université Paris-Est, CERMICS (ENPC), 6–8, Avenue B. Pascal, 77455, Marne la Vallée, France

    Alexandre Ern

Authors
  1. Rita Riedlbeck
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  2. Daniele A. Di Pietro
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  3. Alexandre Ern
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Corresponding author

Correspondence to Rita Riedlbeck .

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Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

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Riedlbeck, R., Di Pietro, D.A., Ern, A. (2017). Equilibrated Stress Reconstructions for Linear Elasticity Problems with Application to a Posteriori Error Analysis. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_22

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