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Journal of Scientific Computing

, Volume 17, Issue 1–4, pp 447–459 | Cite as

A Reduced-Basis Element Method

  • Yvon Maday
  • Einar M. Rønquist
Article

Abstract

Reduced basis methods are particularly attractive to use in order to diminish the number of degrees of freedom associated with the approximation of a set of partial differential equations. The main idea is to construct ad hoc basis functions with a large information content. In this note, we propose to develop and analyze reduced basis methods for simulating hierarchical flow systems, which is of relevance for studying flows in a network of pipes, an example being a set of arteries or veins. We propose to decompose the geometry into generic parts (e.g., pipes and bifurcations), and to contruct a reduced basis for these generic parts by considering representative geometric snapshots. The global system is constructed by gluing the individual basis solutions together via Lagrange multipliers.

partial differential equation reduced basis geometric snapshot spectral element nonconforming 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Yvon Maday
    • 1
  • Einar M. Rønquist
    • 2
  1. 1.Laboratoire d'Analyse NumériqueUniversité Pierre et Marie Curie, Boîte courrier 187ParisFrance
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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