WIAS Preprint No. 1527, (2010)

A posteriori optimization of parameters in stabilized methods for convection-diffusion problems --- Part I



Authors

  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Knobloch, Petr
  • Savescu, Simona B.

2010 Mathematics Subject Classification

  • 65N30

Keywords

  • convection-diffusion problems, stabilized finite element methods, parameter optimization, SUPG method, residual-based error estimator

Abstract

Stabilized finite element methods for convection-dominated problems require the choice of appropriate stabilization parameters. From numerical analysis, often only their asymptotic values are known. This paper presents a general framework for optimizing the stabilization parameters with respect to the minimization of a target functional. Exemplarily, this framework is applied to the SUPG finite element method and the minimization of a residual-based error estimator and error indicator. Benefits of the basic approach are shown and further improvements are discussed.

Appeared in

  • Comput. Methods Appl. Mech. Engrg., 200 (2011) pp. 2916--2929.

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