Numerical solution of the fokker-planck equation by finite difference and finite element methods - A comparative study

L. Pichler, Arif Masud, L. A. Bergman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategies are required for an efficient application to problems of dimension ≥ 3. Recently, a stabilized multi-scale finite element method has been effectively applied to the Fokker-Planck equation effectively by means of a considerably reduction of the required number of elements. 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 languageEnglish (US)
Title of host publicationECCOMAS Thematic Conference - COMPDYN 2011
Subtitle of host publication3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering: An IACM Special Interest Conference, Programme
StatePublished - 2011
Event3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2011 - Corfu, Greece
Duration: May 25 2011May 28 2011

Other

Other3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2011
CountryGreece
CityCorfu
Period5/25/115/28/11

Keywords

  • Duffing oscillator
  • Finite difference method
  • Finite element method
  • Fokker-planck equation
  • Linear oscillator
  • Multi- scale finite element method

ASJC Scopus subject areas

  • Computers in Earth Sciences
  • Geotechnical Engineering and Engineering Geology
  • Computational Mathematics

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