In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth "parametric manifold"-dimension reduction; efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations-rapid convergence; a posteriori error estimation procedures-rigorous and sharp bounds for the linear-functional outputs of interest; and Offline-Online computational decomposition strategies-minimum marginal cost for high performance in the real-time/embedded (e.g., parameter-estimation, control) and many-query (e.g., design optimization, multi-model/scale) contexts. We present illustrative results for heat conduction and convection-diffusion, inviscid flow, and linear elasticity; outputs include transport rates, added mass, and stress intensity factors.
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations / Rozza, Gianluigi; Huynh, D. B. P.; Patera, A. T.. - In: ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING. - ISSN 1134-3060. - 15:3(2008), pp. 229-275. [10.1007/s11831-008-9019-9]
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
Rozza, Gianluigi;
2008-01-01
Abstract
In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth "parametric manifold"-dimension reduction; efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations-rapid convergence; a posteriori error estimation procedures-rigorous and sharp bounds for the linear-functional outputs of interest; and Offline-Online computational decomposition strategies-minimum marginal cost for high performance in the real-time/embedded (e.g., parameter-estimation, control) and many-query (e.g., design optimization, multi-model/scale) contexts. We present illustrative results for heat conduction and convection-diffusion, inviscid flow, and linear elasticity; outputs include transport rates, added mass, and stress intensity factors.File | Dimensione | Formato | |
---|---|---|---|
s11831-008-9019-9.pdf
non disponibili
Tipologia:
Versione Editoriale (PDF)
Licenza:
Non specificato
Dimensione
1.71 MB
Formato
Adobe PDF
|
1.71 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.