Galerkin method for feedback controlled Rayleigh--Bénard convection
- Wagner, Barbara
- 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.
- Nonlinearity, Volume 21 (2008) pp. 2625--2651.