A quasi-optimal sparse grids procedure for groundwater flows

A quasi-optimal sparse grids procedure for groundwater flows

J. Beck, F. Nobile, L. Tamellini, R. Tempone A quasi-optimal sparse grids procedure for groundwater flows. Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012. Selected papers from the ICOSAHOM conference June 25-29, 2012, Gammarth, Tunisia. Lecture Notes in Computational Science and Engineering Volume 95, pp. 1-16, 2014.‚Äč
J. Beck, F. Nobile, L. Tamellini, R. Tempone
Uncertainty Quantification
2014
In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work \On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random fi eld. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its e ectivenenss on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coeffcients of the solution and an effcient nested quadrature rule with respect to the Gaussian weight.
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