Error Estimation and Improvement of Convergence for a Time Stepping Algorithm Based on a Finite Element Approach in Time

Abstract eng:
In seismic engineering either a modal analysis (based on the response spectra method) or a time history analysis may be performed. The response spectra method usually over-estimates the dynamic reactions of the structure. Therefore, the time history analysis is more appropriate if realistic results shall be obtained. In time history analysis the convergence of the times stepping algorithm that is used is of key importance. In the current paper an error estimation is performed for a time stepping algorithm based on a Finite Element approach in time (the so-called Betsch method, see [1] and [2]). The convergence rate of the time stepping algorithm is derived analytically and proofed numerically for different polynomial degrees of the shape functions. In order to increase the convergence rate a 3-step algorithm according to Tarnow [6] is implemented into the Betsch method. This allows high accurate results even when large time steps and only linear shape functions are used.

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