A least‐squares finite element method for incompressible Navier‐Stokes problems

Abstract 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 10 000 and backward‐facing step flow at Reynolds number up to 900.