Robust equilibrated a posteriori error estimators for the Reissner-Mindlin 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 system. We propose a new robust a posteriori error estimator based on H(div ) conforming finite elements and equilibrated fluxes. It is shown that this estimator gives rise to an upper bound where the constant is one up to higher order terms. Lower bounds can also be established with constants depending on the shape regularity of the mesh. The reliability and efficiency of the proposed estimator are confirmed by some numerical tests.

Mots clés: Reissner-Mindlin plate; Finite elements; A posteriori error estimators

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Serge Nicaise, Emmanuel Verhille. Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system. Calcolo, 2011, 48 (4), pp.307-335. ⟨10.1007/s10092-011-0042-0⟩. ⟨hal-00531654⟩