LEAST-SQUARES SOLUTION OF INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITHTHE P-VERSION OF FINITE-ELEMENTS

A p-version of the least-squares finite element method, based on the v elocity-pressure-vorticity formulation, is developed for solving stead y-state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfa ctorily with the conjugate gradient method. In conjunction with the us e of rapid operator application which avoids the formation of both ele ment and global matrices, it is possible to achieve a highly compact a nd efficient solution scheme for the incompressible Navier-Stokes equa tions. Numerical results are presented for two-dimensional flow over a backward-facing step. The effectiveness of simple outflow boundary co nditions is also demonstrated.