Convergence and optimality of the adaptive nonconforming linear element method for the stokes problem

Jun Hu, Jinchao Xu

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi-orthogonality property for both the velocity and the pressure in this saddle point problem, we introduce a new prolongation operator to carry through the discrete reliability analysis for the error estimator. We then use a specially defined interpolation operator to prove that, up to oscillation, the error can be bounded by the approximation error within a properly defined nonlinear approximate class. Finally, by introducing a new parameter-dependent error estimator, we prove the convergence and optimality estimates.

Original languageEnglish (US)
Pages (from-to)125-148
Number of pages24
JournalJournal of Scientific Computing
Volume55
Issue number1
DOIs
StatePublished - Apr 1 2013

Fingerprint

Stokes Problem
Error Estimator
Optimality
Saddle Point Problems
Prolongation
Reliability Analysis
Approximation Error
Operator
Orthogonality
Interpolate
Oscillation
Dependent
Reliability analysis
Estimate
Mathematical operators
Interpolation
Standards
Class

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Convergence and optimality of the adaptive nonconforming linear element method for the stokes problem. / Hu, Jun; Xu, Jinchao.

In: Journal of Scientific Computing, Vol. 55, No. 1, 01.04.2013, p. 125-148.

Research output: Contribution to journalArticle

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