Star-based a posteriori error estimates for elliptic problems.

Boujemaa Achchab (1) , Abdellatif Agouzal (2) , Naima Debit (2) , Khalid Bouihat (1)

1 LERMA - Laboratoire d'Etudes et Recherche en Mathématiques Appliquées
2 MMCS - Modélisation mathématique, calcul scientifique

We give an a posteriori error estimator for nonconforming finite element approximations of diffusion-reaction and Stokes problems, which relies on the solution of local problems on stars. It is proved to be equivalent to the energy error up to a data oscillation, without requiring Helmholtz decomposition of the error nor saturation assumption. Numerical experiments illustrate the good behavior and efficiency of this estimator for generic elliptic problems.

Mots clés: Stokes equations; A posteriori error estimator; nonconforming finite element method; diffusion reaction equations; Stokes equations.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Boujemaa Achchab, Abdellatif Agouzal, Naima Debit, Khalid Bouihat. Star-based a posteriori error estimates for elliptic problems.. Journal of Scientific Computing, 2014, 60 (1), pp.184-202. ⟨10.1007/s10915-013-9793-x⟩. ⟨hal-00690013⟩