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

Application to Transport and Continuum Mechanics
Original Paper

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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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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