A quasi-optimal sparse grids procedure for groundwater flows

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 effectivenenss 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.


Editor(s):
Azaïez, Mejdi
El Fekih, Henda
Hesthaven, Jan S.
Published in:
Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012, 1-16
Presented at:
International Conference on Spectral and High-Order Methods 2012 (ICOSAHOM'12), Gammarth, Tunisia, June 25-29, 2012
Year:
2014
Publisher:
Springer
Keywords:
Note:
Invited Paper. Also available as MATHICSE-report 46-2012
Laboratories:


Note: The status of this file is: EPFL only
PRIVATE


 Record created 2013-04-10, last modified 2018-09-13

Publisher's version:
Download fulltextPDF
code for paper result:
Download fulltextZIP
Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)