Résumé
In this work, we prove what appear to be the first Reynolds-semi-robust and
pressure-robust velocity error estimates for an H(div)-conforming approximation
of unsteady incompressible flows of power-law type fluids. The proposed methods
hinges on a discontinuous Galerkin approximation of the viscous term and a
reinforced upwind-type stabilization of the convective term. The derived
velocity error estimates account for pre-asymptotic orders of convergence
observed in convection-dominated flows through regime-dependent estimates of
the error contributions. A complete set of numerical results validate the
theoretical findings.