Error Analysis of Proper Orthogonal Decomposition Stabilized Methods for Incompressible Flows

Proper orthogonal decomposition (POD) stabilized methods for the Navier--Stokes equations are considered and analyzed. We consider two cases: case in which snapshots based on a non inf-sup stable method an method. For both cases we construct approximations to velocity pressure. first case, analyze scheme with equal order polynomials pressure local projection stabilization (LPS) gradient of POD add same kind LPS as direct method, together grad-div stabilization. In second Galerkin model also apply this since discretely divergence-free, can be removed from formulation approximation velocity. To approximate pressure, needed many engineering applications, use supremizer recovery Error bounds constants independent inverse powers viscosity parameter proved methods. Numerical experiments show accuracy performance schemes.