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Galerkin proper orthogonal decomposition methods for parabolic problems. (English) Zbl 1005.65112
Authors’ abstract: Error estimates for Galerkin proper orthogonal decomposition (POD) methods for linear and certain nonlinear parabolic systems are proved. The resulting error bounds depend on the number of POD basis functions and on the time discretization. Numerical examples are included.

MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
35K15Second order parabolic equations, initial value problems
35K55Nonlinear parabolic equations