FINITE-ELEMENT APPROXIMATIONS OF A LADYZHENSKAYA MODEL FOR STATIONARY INCOMPRESSIBLE VISCOUS-FLOW

Some finite-element approximation procedures are presented for a model proposed by Ladyzhenskaya for stationary incompressible viscous flow. The approximate problems are proved to be well posed and stable under standard assumptions on the finite-element families. The solutions of the approximate problems converge to the solution of the original problem minimum regularity assumptions. Some error estimates are derived. The optimal order of accuracy is assured with, or even without, using exact integration rules in the approximation procedure. Iterative methods for solving the discrete nonlinear problems and comments on some computational experiments are provided. Special attention is also paid to the common properties as well as differences between the approximation procedure presented here and the approximation for the stationary Navier-Stokes equations.