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.
Reviewer: Song Jiang (Beijing)
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 |
