On the unilateral contact between membranes Part 2: A posteriori analysis and numerical experiments

Faker Ben Belgacem (1) , Christine Bernardi (2) , Adel Blouza (2) , Martin Vohralík (2)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne
2 LJLL - Laboratoire Jacques-Louis Lions

The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. A discretization of this system is proposed in Part 1 of this work, where the displacements are approximated by standard finite elements and the action by a local postprocessing which admits an equivalent mixed reformulation.Here, we perform the a posteriori analysis of this discretization and prove optimal error estimates. Next, we present numerical experiments that confirm the efficiency of the error indicators.

Domaines: Analyse numérique [cs.NA]

Faker Ben Belgacem, Christine Bernardi, Adel Blouza, Martin Vohralík. On the unilateral contact between membranes Part 2: A posteriori analysis and numerical experiments. IMA Journal of Numerical Analysis, 2011, 32 (Issue 3), pp.1147-1172. ⟨10.1093/imanum/drr003⟩. ⟨hal-00461144⟩