Convergence of the space-time element method with rectangular elements

The convergence of the space-time element method (STEM) with linear, quadra tic and cubic shape functions in time was studied. A standard procedure use d for examining the convergence of multi-step methods for solving ordinary differential equations was applied. Diagrams of dispersion error and approx imation errors of initial conditions and linear load changes are presented in the paper. It was found that the STEM was free from errors connected wit h algorithmic dissipation. In order to verify the results of theoretical co nsiderations, the STEM was applied with a parabolic shape function to analy ze the vibrations of a system with four degrees of freedom. The results obt ained confirm the great precision of the STEM with non-linear shape functio ns. (C) 2001 Elsevier Science B.V. All rights reserved.