Optimal low order finite element methods for incompressible flow

Abstract In this paper we consider the characterization of optimal stabilisation parameters associated with mixed finite element approximations of Stokes flow. We show how the optimal parameter in terms of the approximating power of the method, is related to the parameter value which minimises the condition number of the associated Schur complement system for the pressure field. We illustrate the tightness of our abstract theoretical results in the cases of the Q 1 - P 0 quadrilateral and P 1 - P 1 triangular elements.