WIAS Preprint No. 1714, (2012)

A robust SUPG norm a posteriori error estimator for the SUPG finite element approximation of stationary convection-diffusion equations



Authors

  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Novo, Julia

2010 Mathematics Subject Classification

  • 65N30

Keywords

  • stationary convection-diffusion equations, SUPG finite element method, error in SUPG norm, a posteriori error estimator, adaptive grid refinement

Abstract

A robust residual-based a posteriori estimator is proposed for the SUPG finite element method applied to stationary convection-diffusion-reaction equations. The error in the natural SUPG norm is estimated. The main concern of this paper is the consideration of the convection-dominated regime. A global upper bound and a local lower bound for the error are derived, where the global upper estimate relies on some hypotheses. Numerical studies demonstrate the robustness of the estimator and the fulfillment of the hypotheses. A comparison to other residual-based estimators with respect to the adaptive grid refinement is also provided.

Appeared in

  • Comput. Methods Appl. Mech. Engrg., 255 (2013) pp. 289--305.

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