A residual local projection method for the Oseen equation

Gabriel Barrenechea, Frédéric Valentin

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

A new residual local projection stabilized method (RELP) is proposed as a result of an enriched Petrov-Galerkin strategy for the Oseen problem. The 12 × l pairs, l = 0, 1 with continuous or discontinuous pressures, are made stable by enhancing them with solutions of residual-based local Oseen problems and performing a static condensation procedure afterward. This process does not involve the numerical solution of the local problems and maintains the degrees of freedom of the original spaces. The method adds symmetric terms to the Galerkin formulation which are easy to implement at the element level. Consistency, well-posedness and error estimates are demonstrated, and an economic way to recover a locally conservative velocity field for the discontinuous pressure case is also proposed. Extensive numerical experiments attest the theoretical results and compare the RELP method to previously existing alternatives.

LanguageEnglish
Pages1906-1921
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume199
Issue number29-32
DOIs
Publication statusPublished - 1 Jun 2010

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projection
economics
Condensation
condensation
velocity distribution
degrees of freedom
formulations
Economics
estimates
Experiments

Keywords

  • stabilized finite element method
  • boundary layer
  • consistent method
  • LPS
  • Oseen equation

Cite this

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A residual local projection method for the Oseen equation. / Barrenechea, Gabriel; Valentin, Frédéric.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 29-32, 01.06.2010, p. 1906-1921 .

Research output: Contribution to journalArticle

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AU - Valentin, Frédéric

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AB - A new residual local projection stabilized method (RELP) is proposed as a result of an enriched Petrov-Galerkin strategy for the Oseen problem. The 12 × l pairs, l = 0, 1 with continuous or discontinuous pressures, are made stable by enhancing them with solutions of residual-based local Oseen problems and performing a static condensation procedure afterward. This process does not involve the numerical solution of the local problems and maintains the degrees of freedom of the original spaces. The method adds symmetric terms to the Galerkin formulation which are easy to implement at the element level. Consistency, well-posedness and error estimates are demonstrated, and an economic way to recover a locally conservative velocity field for the discontinuous pressure case is also proposed. Extensive numerical experiments attest the theoretical results and compare the RELP method to previously existing alternatives.

KW - stabilized finite element method

KW - boundary layer

KW - consistent method

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