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Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations

Rozza, G. / Huynh, D. B. P. / Patera, A. T.

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.

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Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations

Rozza, G. / Huynh, D. B. P. / Patera, A. T.

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.

Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations

Rozza, G. / Huynh, D. B. P. / Patera, A. T.

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.

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Title:

Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations

Contributors:

Rozza, G. (author) / Huynh, D. B. P. (author) / Patera, A. T. (author)

Published in:

Archives of Computational Methods in Engineering ; 15

Publication date:

2008

ISSN:

DOI:

https://doi.org/10.1007/s11831-008-9019-9

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

English

Keywords:

Proper Orthogonal Decomposition , Stress Intensity Factor , Posteriori Error Estimation , Posteriori Error

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