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.
|Title of host publication||Proceedings of the 27th International Symposium on Rarefied Gas Dynamics (Pacific Grove CA, USA, July 10-15, 2010)|
|Editors||D.A. Levin, I.J. Wysong, A.L. Garcia|
|Publisher||American Institute of Physics|
|Publication status||Published - 2011|
|Name||AIP Conference Proceedings|