Approximation of the p-stokes equations with equal-order finite elements - Hirn, Adrian (Journal of mathematical fluid mechanics, 2013)
Non-Newtonian fluid motions are often modeled by the p-Stokes equations with power-law exponent p∈(1,∞)p∈(1,∞){p\in(1,∞)} . 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∈(1,∞)p∈(1,∞){p\in(1,∞)} the well-posedness of the discrete problems is shown and a priori error estimates are proven. For p∈(1,2]p∈(1,2]{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.