A quasi-optimal sparse grids procedure for groundwater flows

Joakim Beck, Fabio Nobile, Lorenzo Tamellini, Raul Tempone*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

14 Scopus citations

Abstract

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 field. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its effectiveness on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and an efficient nested quadrature rule with respect to the Gaussian weight.

Original languageEnglish (US)
Title of host publicationSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 - ICOSAHOM conference, Selected papers
EditorsMejdi Azaïez, Jan S. Hesthaven, Henda El Fekih
PublisherSpringer Verlag
Pages1-16
Number of pages16
ISBN (Electronic)9783319016009
DOIs
StatePublished - Jan 1 2014
Event9th International Conference on Spectral and High Order Methods, ICOSAHOM 2012 - Gammarth, Tunisia
Duration: Jun 25 2012Jun 29 2012

Publication series

NameLecture Notes in Computational Science and Engineering
Volume95
ISSN (Print)1439-7358

Other

Other9th International Conference on Spectral and High Order Methods, ICOSAHOM 2012
CountryTunisia
CityGammarth
Period06/25/1206/29/12

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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