Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force
Abstract
The propagation of charged particles through a scattering medium in the presence of a magnetic field can be described by a Fokker-Planck equation with Lorentz force. This model is studied both, from a theoretical and a numerical point of view. A particular trace estimate is derived for the relevant function spaces to clarify the meaning of boundary values. Existence of a weak solution is then proven by the Rothe method. In the second step of our investigations, a fully practical discretization scheme is proposed based on an implicit Euler method for the energy variable and a spherical-harmonics finite-element discretization with respect to the remaining variables. A complete error analysis of the resulting scheme is given and numerical test are presented to illustrate the theoretical results and the performance of the proposed method.
Keywords
Cite
@article{arxiv.2304.01937,
title = {Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force},
author = {Vincent Bosboom and Herbert Egger and Matthias Schlottbom},
journal= {arXiv preprint arXiv:2304.01937},
year = {2025}
}
Comments
Corresponding code can be found at https://zenodo.org/records/17106062