Convergence of the space-time element method with rectangular elements Original Research Article

The convergence of the space-time element method (STEM) with linear, quadratic and cubic shape functions in time was studied. A standard procedure used for examining the convergence of multi-step methods for solving ordinary differential equations was applied. Diagrams of dispersion error and approximation errors of initial conditions and linear load changes are presented in the paper. It was found that the STEM was free from errors connected with algorithmic dissipation. In order to verify the results of theoretical considerations, the STEM was applied with a parabolic shape function to analyze the vibrations of a system with four degrees of freedom. The results obtained confirm the great precision of the STEM with non-linear shape functions.