A posteriori error estimation for the dual mixed finite element method for the $p$-Laplacian in a polygonal domain

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

1 SIMPAF - SImulations and Modeling for PArticles and Fluids
2 Département de Mathématiques et de Statistiques-Université de Moncton
3 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

For the discrete solution of the dual mixed formulation for the $p$-Laplace equation, we define two residues $R$ and $r$. Then we bound the norm of the errors on the two unknowns in terms of the norms of these two residues. Afterwards, we bound the norms of these two residues by functions of two error estimators whose expressions involve at the very most the datum and the computed quantities. We next explain how the discretized dual mixed formulation is hybridized and solved. We close our paper by numerical tests for $p$=1.8 and $p$=3 firstly to corroborate the orders of convergence established by M. Farhloul and H. Hanouzi [1], and secondly to experimentally verify the reliability of our a posteriori error estimates.

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Mohamed Farhloul, Luc Paquet. A posteriori error estimation for the dual mixed finite element method for the $p$-Laplacian in a polygonal domain. Computer Methods in Applied Mechanics and Engineering, 2007, 196 (25-28), pp.2570-2582. ⟨10.1016/j.cma.2006.11.023⟩. ⟨hal-00768644⟩