Worst-Case Scenario Tools for Verification and Validation

Fabio Nobile
MOX, Dipartimento di Matematica
Politecnico di Milano

Many physical problems are affected by a relatively large uncertainty in the input data and in the coefficients of the underlying mathematical model. In many cases, a full statistical characterization of those uncertainties is impossible to obtain and the only information available is a range where the input data and model coefficients can vary in. Worst-case scenario analysis is a useful tool to include this type of uncertainty in the mathematical model.

We will focus on elliptic PDE's which may feature uncertainty in the coefficients or boundary conditions. Particular attention is devoted to the case of uncertainty in Dirichlet boundary data. The proposed approach for worst-case scenario analysis is based on a perturbation method. It is computationally inexpensive and allows one to account for perturbations in infinite dimensional spaces.

We will present numerical examples showing the effectiveness of the methodology and we will hint about using this technique in the framework of V&V.

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