Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866918145917190144 |
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| author | Bosboom, Vincent Egger, Herbert Schlottbom, Matthias |
| author_facet | Bosboom, Vincent Egger, Herbert Schlottbom, Matthias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01937 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force Bosboom, Vincent Egger, Herbert Schlottbom, Matthias Numerical Analysis 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. |
| title | Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2304.01937 |