Abstract
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’s law with \({\eta _{\infty }=0}\). We give an existence and uniqueness result for the approximate problem and we prove error bounds.
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Sandri, D. Numerical analysis of a four-field model for the approximation of a fluid obeying the power law or Carreau’s law. Japan J. Indust. Appl. Math. 31, 633–663 (2014). https://doi.org/10.1007/s13160-014-0155-3
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DOI: https://doi.org/10.1007/s13160-014-0155-3