Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics

Error estimates for Galerkin proper orthogonal decomposition (POD) methods for nonlinear parabolic systems arising in fluid dynamics are proved. For the time integration the backward Euler scheme is considered. The asymptotic estimates involve the singular values of the POD snapshot set and the grid-structure of the time discretization as well as the snapshot locations.