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.
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