Dynamic time-step estimates for two-dimensional transient field problems using square elements

This study presents an experimental approach to estimate time steps that integrate the two-dimensional field equation over a square element within 5 per cent accuracy from the exact solution. The time-step estimates were determined for three finite element, and three finite difference schemes. Comparisons between finite element and finite difference methods and the various time-stepping schemes were conducted. The dynamic time-step estimates are functions of grid size and the smallest eigenvalue of the system of ODEs, lambda(1). The results indicate that the finite element and finite difference methods generate similar time-step estimates and are at similar accuracy levels. The central difference scheme is superior to the other two schemes as far as the flexibility in allowing larger time step while maintaining the accuracy. The backward difference and the forward difference schemes were very close in their level of accuracy. (C) 1998 John Wiley & Sons, Ltd.