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

Rodolfo Araya, Gabriel R. Barrenechea, Frédéric Valentin

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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.
Original languageEnglish
Pages (from-to)322–348
Number of pages27
JournalSIAM Journal on Numerical Analysis
Volume44
Issue number1
DOIs
Publication statusPublished - 2006

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Keywords

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

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