Stabilized finite element methods based on multiscale enrichment for the Stokes problem

Rodolfo Araya, Gabriel R. Barrenechea, Frédéric Valentin

Research output: Contribution to journal › Article

46 Citations (Scopus)

Abstract

This work concerns the development of stabilized finite element methods for the Stokes problem considering nonstable different (or equal) order of velocity and pressure interpolations. The approach is based on the enrichment of the standard polynomial space for the velocity component with multiscale functions which no longer vanish on the element boundary. On the other hand, since the test function space is enriched with bubble-like functions, a Petrov--Galerkin approach is employed. We use such a strategy to propose stable variational formulations for continuous piecewise linear in velocity and pressure and for piecewise linear/piecewise constant interpolation pairs. Optimal order convergence results are derived and numerical tests validate the proposed methods.
LanguageEnglish
Pages322–348
Number of pages27
JournalSIAM Journal on Numerical Analysis
Volume44
Issue number1
DOIs
Publication statusPublished - 2006

Fingerprint

Stabilized Finite Element Method
Stokes Problem
Finite element method
Piecewise Linear
Interpolation
Interpolate
Petrov-Galerkin
Variational Formulation
Test function
Convergence Results
Function Space
Bubble
Boundary Elements
Vanish
Polynomials
Polynomial

Keywords

  • Stokes equation
  • multiscale functions
  • SIMPLEST element
  • bubble function
  • numerical analysis

Cite this

Araya, Rodolfo ; Barrenechea, Gabriel R. ; Valentin, Frédéric. / Stabilized finite element methods based on multiscale enrichment for the Stokes problem. In: SIAM Journal on Numerical Analysis. 2006 ; Vol. 44, No. 1. pp. 322–348.
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Araya, R, Barrenechea, GR & Valentin, F 2006, 'Stabilized finite element methods based on multiscale enrichment for the Stokes problem' SIAM Journal on Numerical Analysis, vol. 44, no. 1, pp. 322–348. https://doi.org/10.1137/050623176

Stabilized finite element methods based on multiscale enrichment for the Stokes problem. / Araya, Rodolfo; Barrenechea, Gabriel R.; Valentin, Frédéric.

In: SIAM Journal on Numerical Analysis, Vol. 44, No. 1, 2006, p. 322–348.

Research output: Contribution to journal › Article

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AU - Valentin, Frédéric

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N2 - This work concerns the development of stabilized finite element methods for the Stokes problem considering nonstable different (or equal) order of velocity and pressure interpolations. The approach is based on the enrichment of the standard polynomial space for the velocity component with multiscale functions which no longer vanish on the element boundary. On the other hand, since the test function space is enriched with bubble-like functions, a Petrov--Galerkin approach is employed. We use such a strategy to propose stable variational formulations for continuous piecewise linear in velocity and pressure and for piecewise linear/piecewise constant interpolation pairs. Optimal order convergence results are derived and numerical tests validate the proposed methods.

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Araya R, Barrenechea GR, Valentin F. Stabilized finite element methods based on multiscale enrichment for the Stokes problem. SIAM Journal on Numerical Analysis. 2006;44(1):322–348. https://doi.org/10.1137/050623176

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