Approximation of the p-stokes equations with equal-order finite elements

• Verfasst von: Hirn, Adrian [VerfasserIn]
• Titel: Approximation of the p-stokes equations with equal-order finite elements
• Verf.angabe: Adrian Hirn
• Jahr des Originals: 2012
• Umfang: 24 S.
• Fussnoten: First online 01 May 2012 ; Gesehen am 05.09.2017
• Titel Quelle: Enthalten in: Journal of mathematical fluid mechanics
• Jahr Quelle: 2013
• Band/Heft Quelle: 15(2013), 1, S. 65-88
• ISSN Quelle: 1422-6952
• DOI: doi:10.1007/s00021-012-0095-0
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1563197871

Abstract

Non-Newtonian fluid motions are often modeled by the p-Stokes equations with power-law exponent p∈(1,∞)p∈(1,∞){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∈(1,∞)p∈(1,∞){p\in(1,\infty)} 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.