Analysis and Systematic Discretization of a Fokker–Planck Equation with Lorentz Force
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 f...
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| Published in | Journal of computational methods in applied mathematics |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
16.09.2025
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| Online Access | Get full text |
| ISSN | 1609-4840 1609-9389 |
| DOI | 10.1515/cmam-2025-0061 |
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| Summary: | 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 tests are presented to illustrate the theoretical results and the performance of the proposed method. |
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| ISSN: | 1609-4840 1609-9389 |
| DOI: | 10.1515/cmam-2025-0061 |