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Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. (English) Zbl 1075.65118
Summary: 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.

MSC:
65M15Error bounds (IVP of PDE)
35A35Theoretical approximation to solutions of PDE
35K20Second order parabolic equations, initial boundary value problems
35Q30Stokes and Navier-Stokes equations
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
76D05Navier-Stokes equations (fluid dynamics)
76M25Other numerical methods (fluid mechanics)