A NEW FINITE-ELEMENT FORMULATION FOR COMPUTATIONAL FLUID-DYNAMICS .5. CIRCUMVENTING THE BABUSKA-BREZZI CONDITION - A STABLE PETROV-GALERKIN FORMULATION OF THE STOKES PROBLEM ACCOMMODATING EQUAL-ORDER INTERPOLATIONS

A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesses better stability properties than the classical Galerkin/variational method. An error analysis is performed for the case in which both the velocity and pressure are approximated by C**0 interpolations. Combinations of C**0 interpolations which are unstable according to the Babuska-Brezzi condition (e. g. , equal-order interpolations) are shown to be stable and convergent within the present framework. Calculations exhibiting the good behavior of the methodology are presented.