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Error estimates of proper orthogonal decomposition eigenvectors and Galerkin projection for a general dynamical system arising in fluid models |
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| Authors: | Pedro Galán del Sastre Rodolfo Bermejo |
| Institution: | (1) Departamento de Matemática Aplicada al Urbanismo, a la Edificación y al Medio Ambiente, E.T.S.A.M., Universidad Politécnica de Madrid, Avda. Juan de Herrera 4, 28040 Madrid, Spain;(2) Departamento de Matemática Aplicada, E.T.S.I.I., Universidad Politécnica de Madrid, C/ José Gutiérrez Abascal 2, 28006 Madrid, Spain |
| Abstract: | We study estimates for proper orthogonal decomposition eigenvectors and eigenvalues as well as error estimates between the exact solution of a 2D Navier–Stokes model and the numerical approach when the proper orthogonal decomposition method is considered. These estimates are also extended when bifurcation diagram are calculated using the so called p-POD or SPOD methods with a new cut-off criterion to minimize noisy modes produced by the p-POD method. |
| Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 65M60 65L60 65N30 76M10 76M25 37N10 65F15 |
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