Numerical Solution of the Fokker-Planck Equation by Finite Difference and Finite Element Methods - A Comparative Study

L. Pichler; A. Masud; Lawrence Bergman

doi:10.1007/978-94-007-5134-7_5

Numerical Solution of the Fokker-Planck Equation by Finite Difference and Finite Element Methods - A Comparative Study

L. Pichler, A. Masud, Lawrence Bergman

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems; also the application to 4d problems has been addressed. However, due to the enormous increase in computational costs, different strategies are required for efficient application to problems of dimension ≥3. Recently, a stabilized multi-scale finite element method has been effectively applied to the Fokker-Planck equation. Also, the alternating directions implicit method shows good performance in terms of efficiency and accuracy. In this paper various finite difference and finite element methods are discussed, and the results are compared using various numerical examples.

Original language	English (US)
Title of host publication	Computational Methods in Applied Sciences
Publisher	Springer
Pages	69-85
Number of pages	17
DOIs	https://doi.org/10.1007/978-94-007-5134-7_5
State	Published - 2013

Publication series

Name	Computational Methods in Applied Sciences
Volume	26
ISSN (Print)	1871-3033

ASJC Scopus subject areas

Civil and Structural Engineering
Modeling and Simulation
Biomedical Engineering
Computer Science Applications
Fluid Flow and Transfer Processes
Computational Mathematics
Electrical and Electronic Engineering

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10.1007/978-94-007-5134-7_5

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AB - Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems; also the application to 4d problems has been addressed. However, due to the enormous increase in computational costs, different strategies are required for efficient application to problems of dimension ≥3. Recently, a stabilized multi-scale finite element method has been effectively applied to the Fokker-Planck equation. Also, the alternating directions implicit method shows good performance in terms of efficiency and accuracy. In this paper various finite difference and finite element methods are discussed, and the results are compared using various numerical examples.

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Numerical Solution of the Fokker-Planck Equation by Finite Difference and Finite Element Methods - A Comparative Study

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