Convergence Properties of the Finite-Element Method for Béenard Convection in an Infinite Layer
Abstract
A method is proposed for predicting the critical Rayleigh number and cell width for the onset of Benard convection in an infinite horizontal layer. This approach is used to demonstrate the superconvergence of the finite element method for the prediction of a point of coalescence of two symmetry-breaking bifurcations. Extrapolation of the predictions gives a value of the critical Rayleigh number exact to seven significant figures.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- September 1985
- DOI:
- 10.1016/0021-9991(85)90012-9
- Bibcode:
- 1985JCoPh..60..346W
- Keywords:
-
- Convergence;
- Finite Element Method;
- Rayleigh Number;
- Rayleigh-Benard Convection;
- Branching (Mathematics);
- Error Analysis;
- Extrapolation;
- Numerical Stability;
- Predictions;
- Fluid Mechanics and Heat Transfer