Goal-oriented adaptive methods for a Boltzmann-type equation

W. Hoitinga, E.H. Brummelen, van

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Abstract

The Boltzmann equations is an integro-differential equation posed on a high-dimensional position-velocity space. The complexity of the Boltzmann equation in principle prohibits straightforward approximation by the finite-element method. In many applications of the Boltzmann equation, interest is however restricted to one particular goal functional of the solution. In such cases, significant reduction of the computational complexity can be accomplished by means of goal-adaptive refinement strategies. In this paper, we present a goal-oriented error-estimation and adaptive-refinement procedure for a one-dimensional prototype of the Boltzmann model with a collision term that exhibits the essential complexities and characteristics of higher dimensional Boltzmann models.
Original languageEnglish
Title of host publicationProceedings of the 27th International Symposium on Rarefied Gas Dynamics (Pacific Grove CA, USA, July 10-15, 2010)
EditorsD.A. Levin, I.J. Wysong, A.L. Garcia
PublisherAmerican Institute of Physics
Pages81-86
ISBN (Print)978-0-7354-0889-0
DOIs
Publication statusPublished - 2011

Publication series

NameAIP Conference Proceedings
Volume1333
ISSN (Print)0094-243X

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