Hybrid finite element methods for the Signorini problem

Faker Ben Belgacem (1) , Yves Renard (1)

1 MIP - Mathématiques pour l'Industrie et la Physique

We study three mixed linear nite element methods for the numerical simulation of the two-dimensional Signorini problem. Applying Falk's Lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them. Two of these nite elements provide optimal results under reasonable regularity assumptions on the Signorini solution, and the numerical investigation shows that the third method also provides optimal accuracy.

Mots clés: finite element approximation; mixed formulation; variational inequalities; bubble-stabilization

Domaines: Analyse numérique [math.NA]

Faker Ben Belgacem, Yves Renard. Hybrid finite element methods for the Signorini problem. Mathematics of Computation, 2003, 72, pp.1117-1145. ⟨10.1090/S0025-5718-03-01490-X⟩. ⟨hal-00690588⟩