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

Jun Hu, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

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 2013

All Science Journal Classification (ASJC) codes

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

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