Augmented spectral formulation for the Stokes problem with variable viscosity and mixed boundary conditions

被引：0
作者：
C. Bousbiat
Y. Daikh
S. Maarouf
D. Yakoubi
机构：
[1] Université de Jijel,
[2] Laboratoire Analyse,undefined
[3] Optimisation et Traitement de l’Information,undefined
[4] Léonard de Vinci Pôle Universitaire,undefined
[5] Research Center,undefined
来源：
Calcolo | 2023年 / 60卷
关键词：
Stokes equations; Variable viscosity; Augmented formulation; Mixed boundary conditions; Spectral methods; A priori estimates; 35Q30;
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摘要：
This paper deals with the analysis of a new augmented formulation in terms of vorticity, velocity and pressure for the Stokes equations with variable viscosity and mixed boundary conditions. The well-posedness of the continuous problem holds under assumptions on the viscosity. When the domain is a parallelepiped, the spectral discretization is proposed using the Galerkin method with numerical integration. Then, we prove the well-posedness of the obtained discrete problem under the same type of conditions on the viscosity. A priori error estimates is then derived for the three unknowns. Finally, numerical experiments are presented that confirm the interest of the discretization.
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