Analysis of some mixed elements for the Stokes problem

Xiao Liang Cheng*, Weimin Han, Hong Ci Huang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


In this paper we discuss some mixed finite element methods related to the reduced integration penalty method for solving the Stokes problem. We prove optimal order error estimates for bilinear-constant and biquadratic-bilinear velocity-pressure finite element solutions. The result for the biquadratic-bilinear element is new, while that for the bilinear-constant element improves the convergence analysis of Johnson and Pitkäranta (1982). In the degenerate case when the penalty parameter is set to be zero, our results reduce to some related known results proved in by Brezzi and Fortin (1991) for the bilinear-constant element, and Bercovier and Pironneau (1979) for the biquadratic-bilinear element. Our theoretical results are consistent with the numerical results reported by Carey and Krishnan (1982) and Oden et al. (1982).

Original languageEnglish
Pages (from-to)19-35
Number of pages17
JournalJournal of Computational and Applied Mathematics
Issue number1
Publication statusPublished - 6 Nov 1997

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Mixed finite elements
  • Optimal order error estimates
  • Reduced integration penalty method
  • Stokes problem


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