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.
First online 01 May 2012
Gesehen am 05.09.2017