Monte Carlo Finite Volume Element Methods for the Convection-Diffusion Equation with a Random Diffusion Coefficient
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-22
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The paper presents a framework for the construction of Monte Carlo finite volume element method (MCFVEM) for the convection-diffusion equation with a random diffusion coefficient, which is described as a random field.
We first approximate the continuous stochastic field by a finite number of random variables via the Karhunen-Loève expansion and transform the initial stochastic problem into a deterministic one with a parameter in high dimensions.
Then we generate independent identically distributed approximations of the solution by sampling the coefficient of the equation and employing finite volume element variational formulation.
Finally the Monte Carlo (MC) method is used to compute corresponding sample averages.
Statistic error is estimated analytically and experimentally.
A quasi-Monte Carlo (QMC) technique with Sobol sequences is also used to accelerate convergence, and experiments indicate that it can improve the efficiency of the Monte Carlo method.
American Psychological Association (APA)
Zhang, Qian& Zhang, Zhiyue. 2014. Monte Carlo Finite Volume Element Methods for the Convection-Diffusion Equation with a Random Diffusion Coefficient. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-487594
Modern Language Association (MLA)
Zhang, Qian& Zhang, Zhiyue. Monte Carlo Finite Volume Element Methods for the Convection-Diffusion Equation with a Random Diffusion Coefficient. Mathematical Problems in Engineering No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-487594
American Medical Association (AMA)
Zhang, Qian& Zhang, Zhiyue. Monte Carlo Finite Volume Element Methods for the Convection-Diffusion Equation with a Random Diffusion Coefficient. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-487594
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-487594