Level set Methods for Polynomial Chaos expansion of stochastic PDEs outputs

Abstract : 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.