The treatment of the locking phenomenon for a general class of variational inequalities

Leila Slimane (1) , Yves Renard (2)

1 Université de Moncton
2 MIP - Mathématiques pour l'Industrie et la Physique

We present the analysis of a class of variational inequalities depending on a small nonnegative parameter in a singular way, for which direct numerical approximation yield a numerical locking phenomenon. It consists in extending some robust approaches to variational inequalities, mainly, conforming and nonconforming methods. We give general sufficient conditions on the discrete problem insuring a uniform convergence relatively to the small parameter, and consequently avoiding numerical locking.

Mots clés: Variational inequalities; Numerical locking; Signorini problems; Stiff transmission; Nonconforming methods

Domaines: Analyse numérique [math.NA]

Leila Slimane, Yves Renard. The treatment of the locking phenomenon for a general class of variational inequalities. Journal of Computational and Applied Mathematics, 2004, 170, pp.121-143. ⟨10.1016/j.cam.2003.12.044⟩. ⟨hal-00690589⟩