Discretization error estimator for transcient dynamic simulations

Abstract

In this paper, we demonstrate that the concept of error in constitutive relation provides an answer to the problem of error estimation in transient dynamic analysis. The construction of our error measure is based on a reformulation of the transient dynamic problem. From the solution to the discretized model, we build a set of fields, which satisfy the kinematic constraints, the initial conditions and the equilibrium equation exactly. The quality of this numerical solution depends on the extent to which the constitutive relations are satisfied. Our error estimator can be used with explicit as well as implicit time integration schemes. Here, it is first calculated on a simple single-degree-of-freedom linear dynamic problem. Its satisfactory behavior is demonstrated by different tests. Moreover, it is compared with several other indicators from the literature. Next, we explain how this error measure can be applied to problems involving both time and space. Then, preliminary one-dimensional test results for a bar fixed at one end are presented and discussed. Finally, we introduce a new error indicator which turns out to be an indicator of the error on the time integration for the initial reference problem. This indicator enables us to extract from the global error estimation the main contribution, which is relative to the time integration scheme chosen. Then, this quantity is calculated in order to evaluate the error due to the lumped mass assumption for problems solved by the explicit central difference method.