A priori convergence of the Greedy algorithm for the parametrized reduced basis method
Annalisa Buffa; Yvon Maday; Anthony T. Patera; Christophe Prud’homme; Gabriel Turinici
ESAIM: Mathematical Modelling and Numerical Analysis (2012)
- Volume: 46, Issue: 3, page 595-603
- ISSN: 0764-583X
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top- P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal.43 (2011) 1457–1472.
- A. Kolmogorov, Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse. Ann. Math. (2)37 (1936) 107–110.
- Y. Maday, A.T. Patera and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parametric elliptic partial differential equations. J. Sci. Comput.17 (2002) 437–446.
- Y. Maday, A.T. Patera and G. Turinici, Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. C. R. Acad. Sci., Paris, Sér. I Math.335 (2002) 289–294.
- J.M. Melenk, On n-widths for elliptic problems. J. Math. Anal. Appl.247 (2000) 272–289.
- A. Pinkus, n-widths in approximation theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]7. Springer-Verlag, Berlin (1985).
- G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations – application to transport and continuum mechanics. Arch. Comput. Methods Eng.15 (2008) 229–275.
- S. Sen, Reduced-basis approximation and a posteriori error estimation for many-parameter heat conduction problems. Numer. Heat Transfer Part B54 (2008) 369–389.
- K. Veroy, C. Prud’homme, D.V. Rovas and A.T. Patera, A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, in Proceedings of the 16th AIAA Computational Fluid Dynamics Conference (2003) 2003–3847.
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- Toni Lassila, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza, Generalized Reduced Basis Methods and n-width Estimates for the Approximation of the Solution Manifold of Parametric PDEs
- D. Chapelle, A. Gariah, P. Moireau, J. Sainte-Marie, A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation