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GLS methods for Stokes equations under boundary condition of friction type: formulation-analysis-numerical schemes and simulations

Abstract : In this paper, we present in two and three dimensional space Galerkin least squares (GLS) methods allowing the use of equal order approximation for both the velocity and pressure modeling the Stokes equations under Tresca's boundary condition. We propose and analyse two finite element formulations in bounded domains. Firstly, we construct the unique weak solution for each problem by using the method of regularization combined with the monotone operators theory and compactness properties. Secondly, we study the convergence of the finite element approximation by deriving a priori error estimate. Thirdly, we formulate three numerical algorithms namely; projection-like algorithm couple with Uzawa's iteration, the alternative direction method of multiplier and an active set strategy. Finally some numerical experiments are performed to confirm the theoretical findings and the efficiency of the schemes formulated.
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https://hal.archives-ouvertes.fr/hal-03804931
Contributor : Djoko Kamdem Connect in order to contact the contributor
Submitted on : Friday, October 7, 2022 - 3:20:09 AM
Last modification on : Thursday, October 13, 2022 - 3:52:12 AM

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  • HAL Id : hal-03804931, version 1

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Djoko Kamdem, Jonas Koko. GLS methods for Stokes equations under boundary condition of friction type: formulation-analysis-numerical schemes and simulations. SeMA Journal: Bulletin of the Spanish Society of Applied Mathematics, 2022. ⟨hal-03804931⟩

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