MATHICSE Technical Report : 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 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 and


Year:
2012-11
Publisher:
Écublens, MATHICSE
Keywords:
Note:
MATHICSE Technical Report Nr. 46.2012 November 2012
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