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
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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.
Affiliations des auteurs :
Jocelyne Erhel 1 ; Zoubida Mghazli 2 ; Mestapha Oumouni 1, 2
@article{EP_2014_45_a34,
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},
year = {2014},
volume = {45},
doi = {10.1051/proc/201445034},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201445034/}
}
TY - JOUR AU - Jocelyne Erhel AU - Zoubida Mghazli AU - Mestapha Oumouni TI - A combined collocation and Monte Carlo method for advection-diffusion equation of a solute in random porous media JO - ESAIM. Proceedings PY - 2014 SP - 328 EP - 337 VL - 45 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201445034/ DO - 10.1051/proc/201445034 LA - en ID - EP_2014_45_a34 ER -
%0 Journal Article %A Jocelyne Erhel %A Zoubida Mghazli %A Mestapha Oumouni %T A combined collocation and Monte Carlo method for advection-diffusion equation of a solute in random porous media %J ESAIM. Proceedings %D 2014 %P 328-337 %V 45 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201445034/ %R 10.1051/proc/201445034 %G en %F EP_2014_45_a34
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
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