A hybrid high-order method for a class of quasi-Newtonian Stokes equations on general meshes

In this paper, we introduce a hybrid high-order (HHO) discrete scheme for numerically solving a class of incompressible quasi-Newtonian Stokes equations in R². The presented HHO method depends on hybrid discrete velocity unknowns at cells and edges, and pressure unknowns at cells. Benefiting from the hybridization of unknowns, the computation cost can be reduced by the technique of static condensation and the solvability of the static condensation algebra system is proved. Furthermore, we study the HHO scheme by polynomials of arbitrary degrees k (k ≥ 1) on the general meshes and geometries. The unique solvability of the discrete scheme is proved. Additionally, the optimal a priori error estimates for the velocity gradient and pressure approximations are obtained. Finally, we provide several numerical results to verify the good performance of the proposed HHO scheme and confirm the optimal approximation properties on a variety of meshes and geometries.