Approximation of the p-Stokes Equations with Equal-Order Finite Elements

Non-Newtonian fluid motions are often modeled by the p-Stokes equations with power-law exponent $${p\in(1,\infty)}$$ . In the present paper we study the discretization of the p-Stokes equations with equal-order finite elements. We propose a stabilization scheme for the pressure-gradient based on local projections. For $${p\in(1,\infty)}$$ the well-posedness of the discrete problems is shown and a priori error estimates are proven. For $${p\in(1,2]}$$ the derived a priori error estimates provide optimal rates of convergence with respect to the supposed regularity of the solution. The achieved results are illustrated by numerical experiments.