The construction of our error measurement is based on the reformulation of a transient dynamic problem. From the solution to the discretized model, we have built a set of fields which exactly satisfy the kinematic constraints, the initial conditions as well as the equilibrium equation. The quality of this numerical solution depends on the manner in which the constitutive relations are satisfied.

Our error estimator can be used with both explicit and implicit time integration schemes. It is first computed on a simple linear dynamic problem with one degree of freedom, and different tests demonstrate the satisfactory behaviour of this estimator. Moreover, it has been compared with different indicators in the literature.

Next, we explain how to apply the error measurement to problems involving both time and space. The initial unidimensional test results obtained from a cantilever beam, are then presented and discussed.

Lastly, we introduce a new error indicator, which appears as a time integration scheme error indicator for the initial reference problem. This indicator allows to extract from the global error estimation, the main part relative to the time integration scheme chosen. It is then computed in order to evaluate the amount of error relative to the mass matrix lumping hypothesis for problems solved using the the explicit central differences method.

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