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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:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35K55 Nonlinear parabolic equations
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