Abstract
In this chapter, we apply the HHO method to the discretisation of the steady Stokes problem, which models fluid flows where convective inertial forces are small compared to viscous forces. From a physical point of view, the Stokes problem is obtained writing momentum and mass balance equations. In the case of a uniform density fluid, the mass balance translates into a zero-divergence constraint on the velocity, enabling an interpretation as a constrained minimisation (saddle-point) problem with the pressure acting as the Lagrange multiplier; see Remark 8.7. As a consequence, the well-posedness of the Stokes problem hinges on an inf–sup rather than a coercivity condition. This property has to be reproduced at the discrete level, which requires to select the discrete spaces for the velocity and pressure so that the discrete divergence operator from the former to the latter is surjective.
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Di Pietro, D.A., Droniou, J. (2020). Stokes. In: The Hybrid High-Order Method for Polytopal Meshes. MS&A, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-030-37203-3_8
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