Non-Intrusive Polynomial Chaos Expansion for Uncertainty Quantification in Elmer Heat Transfer Simulations

Finite element heat transfer simulations routinely treat material properties and boundaryconditions as deterministic constants, despite the inherent uncertainty in physical measure-ments. This paper outlines a comprehensive framework for applying non-intrusive Poly-nomial Chaos Expansion (PCE) to the open-source Elmer HeatSolver. By treating thesimulator as a black box and utilizing sparse grids, we extract Sobol’ sensitivity indices ana-lytically. This methodology provides actionable tolerancing recommendations by identifyingwhich uncertain input parameters dominate the variance in critical quantities of interest,such as maximum temperature and heat-flux norm.