On setting a pressure datum when computing incompressible flows

The conventional approach to set the pressure level in a finite element discretization of an enclosed, steady, incompressible flow is to discard a continuity residual and set the associated pressure basis function coefficient to a desired value. Two issues surrounding this setting of a pressure datum are explored. First, it is shown that setting a boundary traction at a single node, in lieu of a Dirichlet velocity condition, is a preferred alternative for use with pressure-stabilized finite element methods. Second, it is shown that setting a pressure datum can slow or even stop the convergence of a GMRES-based iterative solver; though by some appearances a solution may appear to be converged, significant local errors in the velocity may exist. Under such circumstances it is preferable to solve the consistent singular system of equations, rather than setting a pressure datum. It is shown that GMRES converges in such cases, implicity setting a pressure level that is determined from the initial guess.