Convergence Properties of the FiniteElement 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 symmetrybreaking 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:
 10.1016/00219991(85)900129
 Bibcode:
 1985JCoPh..60..346W
 Keywords:

 Convergence;
 Finite Element Method;
 Rayleigh Number;
 RayleighBenard Convection;
 Branching (Mathematics);
 Error Analysis;
 Extrapolation;
 Numerical Stability;
 Predictions;
 Fluid Mechanics and Heat Transfer