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

Application to Transport and Continuum Mechanics
Original Paper

DOI: 10.1007/s11831-008-9019-9

Cite this article as:
Rozza, G., Huynh, D.B.P. & Patera, A.T. Arch Computat Methods Eng (2008) 15: 229. doi:10.1007/s11831-008-9019-9

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.

Copyright information

© CIMNE, Barcelona, Spain 2008

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Singapore-MIT Alliance, E4-04-10National University of SingaporeSingaporeSingapore
  3. 3.Massachusetts Institute of TechnologyCambridgeUSA

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