Convergence Analysis for Incompressible Generalized Newtonian Fluid Flows with Nonstandard Anisotropic Growth Conditions

Authors:
Erich Carelli;Jonas Haehnle;Andreas Prohl
Affiliations:
carelli@na.uni-tuebingen.de and haehnle@na.uni-tuebingen.de and prohl@na.uni-tuebingen.de;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

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Abstract

We study equations to describe incompressible generalized Newtonian fluids, where the extra stress tensor satisfies a nonstandard anisotropic asymptotic growth condition. An implicit finite element discretization and a simple, fully practical fixed-point scheme with proper thresholding criterion are proposed, and convergence toward weak solutions of the limiting problem is shown. Computational experiments are included, which motivate nontrivial fluid flow behavior.