No 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 onedimensional prototype of the Boltzmann model with a collision term that exhibits the essential complexities and characteristics of higher dimensional Boltzmann models.

No abstract

No abstract