Abstract. In this paper, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. The discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. A priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved.

Dans ce travail on a proposé etétudié une formulation mixteà trois champs pour résoudre le problème de Stokes avec des conditions aux limites non-linéaires, du type Tresca. Deux multiplicateurs de Lagrange ontété utilisés afin d'imposer div(u) = 0 et de régulariser la fonctionnelleénergie. Leséléments finis P1 bulle/P1-P1 ont permis de discrétiser le problème résultant. Des estimations d'erreurs ontété dérivées et plusieurs tests numériques sont réalisés. AbstractIn this work we propose and study a three field mixed formulation for solving the Stokes problem with Tresca-type non-linear boundary conditions. Two Lagrange multipliers are used to enforce div(u) = 0 constraint and to regularize the energy functional. The resulting problem is discretised using P1 bubble/P1-P1 finite elements. Error estimates are derived and several numerical studies are achieved.