Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents

A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress exponents p > 2dd+2. The Dirichlet boundary condition is imposed strongly, using any discretization of the boundary data which converges at a sufficient rate. A priori error estimates for velocity vector field and kinematic pressure are derived and numerical experiments are conducted. These confirm the quasi-optimality of the a priori error estimate for the velocity vector field. The a priori error estimates for the kinematic pressure are quasi-optimal if p 2.