Numerical Approximation of a Quasi-Newtonian Stokes Flow Problem with Defective Boundary Conditions

In this article we study the numerical approximation of a quasi-Newtonian Stokes flow problem where only the flow rates are specified at the inflow and outflow boundaries. A variational formulation of the problem, using Lagrange multipliers to enforce the stated flow rates, is given. Existence and uniqueness of the solution to the continuous, and discrete, variational formulations is shown. An error analysis for the numerical approximation is also given. Numerical computations are included which demonstrate the approximation scheme studied.