WIAS Preprint No. 907, (2004)

Galerkin method for feedback controlled Rayleigh--Bénard convection


  • Wagner, Barbara
    ORCID: 0000-0001-8306-3645
  • Münch, Andreas

2010 Mathematics Subject Classification

  • 74D10 74F05 74F10 77N25


  • Galerkin approximation, Stability, Pattern Formation




We employ a Galerkin approximation for the system of equations governing Rayleigh-Bénard convection. This approximation reduces the dimension of the problem by one, while it captures the nonlinear behavior even when only a few basis functions are used. We prove convergence of the method and finally demonstrate the effectiveness of this method for the problems of feedback controlled Rayleigh-Bénard convection in three dimensions and the complex dynamics of spiral-defect chaos.

Appeared in

  • Nonlinearity, Volume 21 (2008) pp. 2625--2651.

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