A combined collocation and Monte Carlo method for advection-diffusion equation of a solute in random porous media

DOI10.1051/proc/201445034zbMath1339.65189OpenAlexW2122338737MaRDI QIDQ3465870

Mestapha Oumouni, Jocelyne Erhel, Zoubida Mghazli

Publication date: 29 January 2016

Published in: ESAIM: Proceedings and Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/proc/201445034

zbMATH Keywords

Monte Carlo methodadvection-diffusion equationcollocation techniquesuncertainty quantificationelliptic PDE with random coefficientsEuler scheme for SDEanisotropic sparse grids

Mathematics Subject Classification ID

Monte Carlo methods (65C05) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Spectral methods applied to problems in fluid mechanics (76M22) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (1)

Physical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansions

Cites Work

• Weak truncation error estimates for elliptic PDEs with lognormal coefficients
• Calculation of the expectation of the solution of a one-dimensional stochastic PDE using a reduced base
• Numerical Analysis of the Advection-Diffusion of a Solute in Porous Media with Uncertainty
• Convergence analysis of macro spreading in 3D heterogeneous porous media
• Mixed and Hybrid Finite Element Methods
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

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