Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem

Gabriel Barrenechea; Frédéric Valentin

doi:10.1016/j.crma.2005.09.038

Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem

Gabriel Barrenechea, Frédéric Valentin

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous finite element space enriched with multiscale functions. The stabilization parameter is related with the enrichment functions which are analytically computed from a boundary value problem at the element level leading to a method which is free of constants. Optimal error estimates are obtained in natural norms and numerical tests validate the method

Original language	English
Pages (from-to)	635-640
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	341
Issue number	10
DOIs	https://doi.org/10.1016/j.crma.2005.09.038
Publication status	Published - 15 Nov 2005

Keywords

Stokes problem
finite element methods
multiscale enrichment

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10.1016/j.crma.2005.09.038

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abstract = "We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous finite element space enriched with multiscale functions. The stabilization parameter is related with the enrichment functions which are analytically computed from a boundary value problem at the element level leading to a method which is free of constants. Optimal error estimates are obtained in natural norms and numerical tests validate the method",

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AU - Valentin, Frédéric

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N2 - We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous finite element space enriched with multiscale functions. The stabilization parameter is related with the enrichment functions which are analytically computed from a boundary value problem at the element level leading to a method which is free of constants. Optimal error estimates are obtained in natural norms and numerical tests validate the method

AB - We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous finite element space enriched with multiscale functions. The stabilization parameter is related with the enrichment functions which are analytically computed from a boundary value problem at the element level leading to a method which is free of constants. Optimal error estimates are obtained in natural norms and numerical tests validate the method

KW - Stokes problem

KW - finite element methods

KW - multiscale enrichment

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IS - 10

ER -

Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem

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Keywords

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