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

作者：Hirn Adrian^*

来源：Journal of Mathematical Fluid Mechanics, 2013, 15(1): 65-88.

DOI：10.1007/s00021-012-0095-0

• Non-Newtonian fluids
• shear-rate-dependent viscosity
• finite element method
• local projection stabilization
• error analysis

Non-Newtonian fluid motions are often modeled by the p-Stokes equations with power-law exponent . 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 the well-posedness of the discrete problems is shown and a priori error estimates are proven. For 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.

• 出版日期2013-3