Numerical analysis of a four-field model for the approximation of a fluid obeying the power law or Carreau%26apos;s law

作者：Sandri D^*

来源：Japan Journal of Industrial and Applied Mathematics, 2014, 31(3): 633-663.

DOI：10.1007/s13160-014-0155-3

• Non-Newtonian fluids
• Finite element methods
• A posteriori error estimates

We study a finite element approximation of a non-linear four-field version of the Stokes system for incompressible fluids. One obtains such a problem when one considers a White-Metzner-type model for a viscoelastic fluid flow and one sets the relaxation time to zero. The non-linear aspect comes from the fact that the viscosity of the fluid obeys the power law or Carreau%26apos;s law with eta(infinity) = 0. We give an existence and uniqueness result for the approximate problem and we prove error bounds.

• 出版日期2014-11