Robust residual a posteriori error estimators for the Reissner-Mindlin eigenvalues system

Emmanuel Creusé (1) , Serge Nicaise (2) , Emmanuel Verhille (3)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
3 LPP - Laboratoire Paul Painlevé - UMR 8524

We consider a conforming finite element approximation of the Reissner-Mindlin eigenvalue system, for which a robust a posteriori error estimator for the eigenvector and the eigenvalue errors is proposed. For that purpose, we first perform a robust a priori error analysis without strong regularity assumption. Upper and lower bounds are then obtained up to higher order terms that are super convergent, provided that the eigenvalue is simple. The convergence rate of the proposed estimator is confirmed by a numerical test.

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Serge Nicaise, Emmanuel Verhille. Robust residual a posteriori error estimators for the Reissner-Mindlin eigenvalues system. Journal of Numerical Mathematics, 2013, 21 (2), pp.89-134. ⟨10.1515/jnum-2013-0004⟩. ⟨hal-00777682v2⟩