Numerical approximation of viscoelastic fluids

@article{Perrotti2017NumericalAO,
  title={Numerical approximation of viscoelastic fluids},
  author={Lou Perrotti and Noel J. Walkington and Daren Wang},
  journal={Mathematical Modelling and Numerical Analysis},
  year={2017},
  volume={51},
  pages={1119-1144}
}
Stable finite element schemes are developed for the solution of the equations modeling the flow of viscoelastic fluids. In contrast with classical statements of these equations, which introduce the stress as a primary variable, these schemes explicitly involve the deformation tensor and elastic energy. Energy estimates and existence of solutions to the discrete problem are established for schemes of arbitrary order without any restrictions on the time step, mesh size, or Weissenberg number… 
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