The Stochastic Galerkin Method for Darcy Flow Problem with Log-Normal Random

0482834 - ÚGN 2018 RIV SK eng J - Journal Article
Beres, Michal - Domesová, Simona
The Stochastic Galerkin Method for Darcy Flow Problem with Log-Normal Random.
Advances in Electrical and Electronic Engineering. Roč. 15, č. 2 (2017), s. 267-279. ISSN 1336-1376
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : Darcy flow * Gaussian random field * Karhunen-Loeve decomposition * polynomial chaos * Stochastic Galerkin method
OECD category: Applied mathematics
http://advances.utc.sk/index.php/AEEE/article/view/2280

This article presents a study of the Stochastic Galerkin Method (SGM) applied to the Darcy flow problem with a log-normally distributed random material field given by a mean value and an autocovariance function. We divide the solution of the problem into two parts. The first one is the decomposition of a random field into a sum of products of a random vector and a function of spatial coordinates, this can be achieved using the Karhunen-Loeve expansion. The second part is the solution of the problem using SGM. SGM is a simple extension of the Galerkin method in which the random variables represent additional problem dimensions. For the discretization of the problem, we use a finite element basis for spatial variables and a polynomial chaos discretization for random variables. The results of SGM can be utilised for the analysis of the problem, such as the examination of the average flow, or as a tool for the Bayesian approach to inverse problems.
Permanent Link: http://hdl.handle.net/11104/0278234