A posteriori error estimates of the stabilized Crouzeix-Raviart finite element method for the Lamé-Navier equations

Emmanuel Creusé (1, 2) , Mohamed Farhloul (3) , Serge Nicaise (4) , Luc Paquet (4)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 Département de Mathématiques et de Statistiques-Université de Moncton
4 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

We obtain a posteriori error estimates for a variant of (non-locking) stabilized non-conforming methods based on the Crouzeix-Raviart element introduced by P. Hansbo and M.G. Larson in [M2AN 37 (2003) 63-72]. We derive upper and lower a posteriori error bounds which are robust with respect to the nearly incompressible materials.

Mots clés: Crouzeix-Raviart element; nonconforming method; stabilized method; nonlocking; a posteriori error estimates

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Mohamed Farhloul, Serge Nicaise, Luc Paquet. A posteriori error estimates of the stabilized Crouzeix-Raviart finite element method for the Lamé-Navier equations. Far East Journal of Mathematical Sciences, 2015, 96 (2), pp.167-192. ⟨10.17654/FJMSJan2015_167_192⟩. ⟨hal-00777678⟩