Finite element approximation of flow of fluids with shear-rate- and pressure-dependent viscosity

@article{Hirn2012FiniteEA,
  title={Finite element approximation of flow of fluids with shear-rate- and pressure-dependent viscosity},
  author={Adriano Hirn and Martin Lanzend{\"o}rfer and Jan Stebel},
  journal={Ima Journal of Numerical Analysis},
  year={2012},
  volume={32},
  pages={1604-1634}
}
We consider a class of incompressible viscous fluids, with the viscosity dependent on shear rate and pressure. We deal with the isothermal steady flow and analyze the Galerkin discretization of the corresponding equations. We discuss the existence and uniqueness of discrete solutions, and their convergence to the solution to the original problem. In particular, we derive a priori error estimates which provide optimal rates of convergence with respect to the expected regularity of the solution… 

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