A stabilized finite element analysis for a power-law pseudoplastic Stokes problem

Abstract

In this work, we present a mixed stabilized finite element formulation in primitive variables, for an incompressible stationary generalized Stokes problem for pseudoplastic flow governed by the Power-Law model. The mixed formulation is constructed by adding least squares of the governing equations to the classical Galerkin formulation, with continuous interpolations for the velocity and discontinuous interpolations for the pressure. A finite element analysis is presented establishing stability conditions and finding error estimates. Numerical results are presented to show the good performance of this formulation and to confirm the mathematical estimates obtained.

Keywords:

• stabilized finite element method
• pseudoplasticity
• equal-order interpolations
• numerical analysis
• non-Newtonian fluids

AMS Subject Classifications:

• 65N30
• 76M10