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 Þeld equation over a square element within 5 per cent accuracy from the exact solution. The time-step estimates were determined for three Þnite element, and three Þnite di¤erence schemes. Comparisons between Þnite element and Þnite di¤erence 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, j1 . The results indicate that the Þnite element and Þnite di¤erence methods generate similar time-step estimates and are at similar accuracy levels. The central di¤erence scheme is superior to the other two schemes as far as the ßexibility in allowing larger time step while maintaining the accuracy. The backward di¤erence and the forward di¤erence schemes were very close in their level of accuracy