| Abstract: | We propose two timestep selection algorithms, based on feedback control theory, for finite element simulation of steady state and transient 2D viscous flow and coupled reaction–convection–diffusion processes. To illustrate performance of the schemes in practice, we solve Rayleigh–Benard–Marangoni flows, flow across a backward‐facing step, unsteady flow around a circular cylinder and chemical reaction systems. Numerical experiments confirm that the feedback controllers produce in some cases a very smooth stepsize variation, suggesting that robust control algorithms are possible. These experiments also show that parameter selection can improve timesteps when co‐ordinated with the convergence control of non‐linear iterations. Further, computational cost of the selection procedures is negligible, since they involve only storing a few extra vectors, computation of norms and evaluation of kinetic energy. Copyright © 2004 John Wiley & Sons, Ltd. |
