Pressure stabilization of finite element approximations of time-dependent incompressible flow problems

Gabriel Barrenechea, Jordi Blasco

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This paper we develop and analyze pressure stabilized, finite element methods for the solution of the transient Stokes problem, which is a linear model problem of transient incompressible flow. A model for the bubble enrichment is proposed to stabilize the numerical solution and an implicit backward Euler method is considered for the time approximation. Different methods are obtained depending on whether bubbles are allowed to evolve with time or they are considered quasi-static. Stability estimates are provided for the two methods considered, both for the velocity and the pressure solutions. Numerical results obtained on test cases are also given, which confirm the theoretical stability results.
LanguageEnglish
Pages219-231
Number of pages13
JournalComputer Methods in Applied Mechanics and Engineering
Volume197
Issue number1-4
DOIs
Publication statusPublished - 1 Dec 2007

Fingerprint

incompressible flow
Incompressible flow
bubbles
Stabilization
stabilization
approximation
finite element method
Finite element method
estimates

Keywords

  • finite elements
  • incompressible flow
  • time-dependent Stokes problem
  • stability analysis
  • pressure stabilization

Cite this

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abstract = "This paper we develop and analyze pressure stabilized, finite element methods for the solution of the transient Stokes problem, which is a linear model problem of transient incompressible flow. A model for the bubble enrichment is proposed to stabilize the numerical solution and an implicit backward Euler method is considered for the time approximation. Different methods are obtained depending on whether bubbles are allowed to evolve with time or they are considered quasi-static. Stability estimates are provided for the two methods considered, both for the velocity and the pressure solutions. Numerical results obtained on test cases are also given, which confirm the theoretical stability results.",
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Pressure stabilization of finite element approximations of time-dependent incompressible flow problems. / Barrenechea, Gabriel; Blasco, Jordi.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 197, No. 1-4, 01.12.2007, p. 219-231.

Research output: Contribution to journalArticle

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AU - Blasco, Jordi

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AB - This paper we develop and analyze pressure stabilized, finite element methods for the solution of the transient Stokes problem, which is a linear model problem of transient incompressible flow. A model for the bubble enrichment is proposed to stabilize the numerical solution and an implicit backward Euler method is considered for the time approximation. Different methods are obtained depending on whether bubbles are allowed to evolve with time or they are considered quasi-static. Stability estimates are provided for the two methods considered, both for the velocity and the pressure solutions. Numerical results obtained on test cases are also given, which confirm the theoretical stability results.

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