MATHICSE-GroupBeck, JoakimNobile, FabioTamellini, LorenzoTempone, Raúl2019-01-222019-01-222019-01-222012-11-0110.5075/epfl-MATHICSE-263218https://infoscience.epfl.ch/handle/20.500.14299/153689In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work \On the optimal polynomial ap- proximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construc- tion of such quasi-optimal grid and show its effectivenenss on a numerical ex- ample. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution andUncertainty QuantificationPDEs with random datalinear elliptic equationsDarcy equationlognormal permeabilityKarhunen-LoèveStochastic Collocation methodsSparse grids approximationtext::working paper