Robust control of PGD-based numerical simulations
Résumé
In this paper, we develop an error estimator that enables to control effectively the quality of numerical solutions obtained using proper generalised decomposition. The method is based on the Constitutive Relation Error and the construction of associated admissible fields. It takes all error sources (discretisations, truncation of the modal representation, etc.) into account and can be used, introducing adjoint-based techniques, for goal-oriented error estimation. Furthermore, specific indicators can be derived to split error contributions and thus drive adaptive procedures in an optimal manner.