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

In this paper, we present 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 discretizations.Firstly, we construct the unique weak solution for each problem by using the method of regularization combined with monotone theory operators and compactness properties.Secondly, we study the convergence of the finite element approximation by estimating the a priori error.Thirdly, for the computation of the finite element solution, we formulate three algorithms namely; projection like algorithm couple with Uzawa iteration, the alternative direction method of multiplier and a active set strategy. Finally some numerical experiments are performed to confirm the theoretical findings and the efficiency of the schemes formulated