A LEAST-SQUARES FINITE-ELEMENT METHOD FOR INCOMPRESSIBLE NAVIER-STOKES PROBLEMS

A least-squares finite element method based on the velocity-pressure-vorticity formulation was proposed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to the saddle point problem of the classic mixed method and can thus accommodate equal-order interpolations. The method has no parameter to tune. The associated algebraic system is symmetric and positive definite. In order to show the validity of the method for high-Reynolds-number problems, this paper provides numerical results for cavity flow at Reynolds number up to 10000 and backward-facing step flow at Reynolds number up to 900.