A Penalty and Extrapolation Method for the Stationary Stokes Equations

A penalty method is set forth for approximating the solution of the stationary Stokes equations that avoids the necessity of having a nondivergent trial function or a trial function that vanishes on the boundary. The penalty method is combined with extrapolation to improve the order of accuracy of the approximate solution while using matrices with lower condition numbers than arise in the simple penalty method.