Geodesic
A combined collocation and Monte Carlo method for advection-diffusion equation of a solute in random porous media
Jocelyne Erhel1 ; Zoubida Mghazli2 ; Mestapha Oumouni1, 2
1 INRIA-SAGE Rennes France
2 LIRNE-IMA Kenitra Morocco
ESAIM. Proceedings, Tome 45 (2014), pp. 328-337.

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In this work, we present a numerical analysis of a method which combines a deterministic and a probabilistic approaches to quantify the migration of a contaminant, under the presence of uncertainty on the permeability of the porous medium. More precisely, we consider the flow equation in a random porous medium coupled with the advection-diffusion equation. Quantities of interest are the mean spread and the mean dispersion of the solute. The means are approximated by a quadrature rule, based on a sparse grid defined by a truncated Karhunen-Loève expansion and a stochastic collocation method. For each grid point, the flow model is solved with a mixed finite element method in the physical space and the advection-diffusion equation is solved with a probabilistic Lagrangian method. The spread and the dispersion are expressed as functions of a stochastic process. A priori error estimates are established on the mean of the spread and the dispersion. Keywords: Uncertainty quantification, elliptic PDE with random coefficients, advection-diffusion equation, collocation techniques, anisotropic sparse grids, Monte Carlo method, Euler scheme for SDE.
DOI : 10.1051/proc/201445034

Jocelyne Erhel 1 ; Zoubida Mghazli 2 ; Mestapha Oumouni 1, 2

1 INRIA-SAGE Rennes France
2 LIRNE-IMA Kenitra Morocco 
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     author = {Jocelyne Erhel and Zoubida Mghazli and Mestapha Oumouni},
     title = {A combined collocation and {Monte} {Carlo} method for advection-diffusion equation of a solute in random porous media},
     journal = {ESAIM. Proceedings},
     pages = {328--337},
     publisher = {mathdoc},
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     year = {2014},
     doi = {10.1051/proc/201445034},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201445034/}
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Jocelyne Erhel; Zoubida Mghazli; Mestapha Oumouni. A combined collocation and Monte Carlo method for advection-diffusion equation of a solute in random porous media. ESAIM. Proceedings, Tome 45 (2014), pp. 328-337. doi : 10.1051/proc/201445034. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445034/

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