A least-squares finite-element method for viscoelastic fluids

We present a least-squares finite element method for the steady Oldroyd type viscoelastic fluids. The nonlinear iteration is coupled with global mesh refinement, and locally weighted norms are used to mitigate effects of boundary singularities. Discretization accuracy in a meaningful normis shown to be optimal when using conforming piecewise polynomial elements for the velocity, pressure and extra stress, and Raviart-Thomas finite elements for the total stress. Numerical results are given for an Oldroyd-B fluid in a 4-1 planar contraction. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)