2014
DOI: 10.1051/m2an/2014001
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Error estimates for Stokes problem with Tresca friction conditions

Abstract: 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… Show more

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Cited by 36 publications
(40 citation statements)
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References 25 publications
(30 reference statements)
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“…We will always assume that γ D = / 0 and γ C = / 0. The existence of an unique (weak) solution component u is proved in [1]. The existence of an unique p is guaranteed, e.g., when γ N = / 0 [4] ALGEBRAIC FORMULATIONS…”
Section: Formulation Of the Model Problemmentioning
confidence: 99%
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“…We will always assume that γ D = / 0 and γ C = / 0. The existence of an unique (weak) solution component u is proved in [1]. The existence of an unique p is guaranteed, e.g., when γ N = / 0 [4] ALGEBRAIC FORMULATIONS…”
Section: Formulation Of the Model Problemmentioning
confidence: 99%
“…The inf-sup stability of the Lagrange multipliers is proved in [1] for the P1-bubble/P1 finite elements. In the case of the P2/P1 finite elements, the stability is observed experimentally, if the friction effect is considered at vertices of triangles lying on γ C [8].…”
Section: Numerical Experimentsmentioning
confidence: 99%
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“…The numerical investigation of these later problems have benefited a lot from the existing knowledge of general ways of treating variational inequalities and some works worth to be mentioned here include [2,7,18,30,39,40].…”
Section: Introductionmentioning
confidence: 99%