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arXiv · 2304.01937

Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force

Vincent Bosboom·Herbert Egger·Matthias Schlottbom
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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.

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Vincent Bosboom, Herbert Egger, Matthias Schlottbom. 2023-04-04. Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force. https://doi.org/10.1515/cmam-2025-0061

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