Abstract
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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Bousbiat, C., Daikh, Y., Maarouf, S. et al. Augmented spectral formulation for the Stokes problem with variable viscosity and mixed boundary conditions. Calcolo 60, 36 (2023). https://doi.org/10.1007/s10092-023-00530-8
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DOI: https://doi.org/10.1007/s10092-023-00530-8
Keywords
- Stokes equations
- Variable viscosity
- Augmented formulation
- Mixed boundary conditions
- Spectral methods
- A priori estimates