An unusual stabilized finite element method for a generalized Stokes problem

G.R. Barrenechea, F. Valentin

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

An unusual stabilized finite element is presented and analyzed herein for a generalized Stokes problem with a dominating zeroth order term. The method consists in subtracting a mesh dependent term from the formulation without compromising consistency. The design of this mesh dependent term, as well as the stabilization parameter involved, are suggested by bubble condensation. Stability is proven for any combination of velocity and pressure spaces, under the hypotheses of continuity for the pressure space. Optimal order error estimates are derived for the velocity and the pressure, using the standard norms for these unknowns. Numerical experiments confirming these theoretical results, and comparisons with previous methods are presented.
Original languageEnglish
Pages (from-to)653-677
Number of pages24
JournalNumerische Mathematik
Volume92
Issue number4
DOIs
Publication statusPublished - 2002

Keywords

  • numerical mathematics
  • Stokes problem
  • finite element method

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