A PENALTY FINITE-ELEMENT METHOD FOR NON-NEWTONIAN CREEPING FLOWS

In this paper we present an iterative penalty finite element method fo r viscous non-Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the soluti on obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty p arameters the iterates converge to the incompressible solution. The ob jective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non-li nearity arising from the constitutive law of non-Newtonian fluids. Som e numerical experiments are conducted in order to assess the performan ce of the approach for fluids whose viscosity obeys the power law.