A Posteriori Error Estimators for the Stokes and Oseen Equations

  • Authors:

  • Mark Ainsworth;J. Tinsley Oden

  • Affiliations:

  • -;-

  • Venue:
  • SIAM Journal on Numerical Analysis
  • Year:
  • 1997

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Abstract

The problem of obtaining /posteriori/ estimates of the discretization error when one uses finite element methods to approximate problems with an incompressibility constraint is discussed. A general approach to the treatment of the constraint condition and to the (possible) non-self-adjointness of the associated momentum equations is presented. A posteriori error estimates are derived for adaptive h, p, and h-p type finite element schemes. Key features are that the local error residual problems are not subject to an incompressibility constraint thereby avoiding the need for special finite element schemes and that the analysis is valid for essentially any discretization scheme, including continuous and discontinuous pressure spaces. The estimator bounds the actual error measured in an energy-like norm.