Level set Methods for Polynomial Chaos expansion of stochastic PDEs outputs

Pierre Sochala (1) , Olivier Le Maitre (2)

1 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)
2 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur

We propose a new method to approximate stochastic solutions of uncertain PDEs using Polynomial Chaos expansions of their level sets. The method is non-intrusive and targets solutions with steep gradients with random locations. An adaptive choice of the level set is used to control the approximation error, ensuring high accuracy at a significantly lower cost compared to classical non-intrusive projection approach. We apply and validate the method on subsurface flows exhibiting steep fronts.

Domains: Mathematics [math]; Analysis of PDEs [math.AP]

Pierre Sochala, Olivier Le Maitre. Level set Methods for Polynomial Chaos expansion of stochastic PDEs outputs. SIAM conference on Uncertainty quantification, SIAM, Apr 2016, Lausanne, Switzerland. ⟨hal-01266242⟩