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.
2008
15
3
229
275
10.1007/s11831-008-9019-9
Rozza, Gianluigi; Huynh, D. B. P.; Patera, A. T.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12327
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