Journal of Scientific Computing

, Volume 17, Issue 1–4, pp 437–446 | Cite as

A Priori Convergence Theory for Reduced-Basis Approximations of Single-Parameter Elliptic Partial Differential Equations

  • Yvon Maday
  • Anthony T. Patera
  • Gabriel Turinici

Abstract

We consider “Lagrangian” reduced-basis methods for single-parameter symmetric coercive elliptic partial differential equations. We show that, for a logarithmic-(quasi-)uniform distribution of sample points, the reduced–basis approximation converges exponentially to the exact solution uniformly in parameter space. Furthermore, the convergence rate depends only weakly on the continuity-coercivity ratio of the operator: thus very low-dimensional approximations yield accurate solutions even for very wide parametric ranges. Numerical tests (reported elsewhere) corroborate the theoretical predictions.

reduced basis method interpolation methods exponential convergence 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Yvon Maday
    • 1
  • Anthony T. Patera
    • 2
  • Gabriel Turinici
    • 3
  1. 1.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie Curie, Boîte courrier 187ParisFrance
  2. 2.Department of Mechanical EngineeringM.I.T.Cambridge
  3. 3.ASCI-CNRS Orsay, and INRIA Rocquencourt M3N, B.P. 105Le ChesnayFrance

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