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 inJournal of computational methods in applied mathematics
Main Authors Bosboom, Vincent, Egger, Herbert, Schlottbom, Matthias
Format Journal Article
LanguageEnglish
Published 16.09.2025
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ISSN1609-4840
1609-9389
DOI10.1515/cmam-2025-0061

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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 tests are presented to illustrate the theoretical results and the performance of the proposed method.
AbstractList 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.
Author Bosboom, Vincent
Schlottbom, Matthias
Egger, Herbert
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Cites_doi 10.1142/S0218202508002784
10.2172/800993
10.1007/978-0-387-70914-7
10.1088/2057-1976/abd239
10.1142/S021820251150014X
10.1137/15M1051336
10.1016/B978-0-12-386944-9.50023-6
10.3934/krm.2012.5.485
10.1016/j.jmaa.2013.04.063
10.1103/RevModPhys.15.1
10.1118/1.4905041
10.1007/978-3-540-85369-5_5
10.1118/1.4937933
10.1142/S0218202510004386
10.1016/j.jmaa.2022.126946
10.1080/00411458708204307
10.1137/1.9780898719208
10.1142/S021820259200003X
10.1088/1361-6560/acf4de
10.1088/0031-9155/51/3/013
10.1090/conm/586/11649
10.1007/978-3-0348-0513-1
10.1088/0031-9155/51/9/010
10.1007/978-1-4612-1994-1
10.1118/1.597920
10.1017/CBO9780511618833
10.1137/S0036142998344706
10.1088/0031-9155/60/13/4963
10.1007/978-3-662-25839-2_2
10.24033/asens.1516
10.1007/BF02165003
10.1088/1361-6560/ab9efe
10.1088/0031-9155/55/3/002
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References 2025091821510448511_j_cmam-2025-0061_ref_009
2025091821510448511_j_cmam-2025-0061_ref_008
2025091821510448511_j_cmam-2025-0061_ref_003
2025091821510448511_j_cmam-2025-0061_ref_025
2025091821510448511_j_cmam-2025-0061_ref_002
2025091821510448511_j_cmam-2025-0061_ref_024
2025091821510448511_j_cmam-2025-0061_ref_001
2025091821510448511_j_cmam-2025-0061_ref_023
2025091821510448511_j_cmam-2025-0061_ref_022
2025091821510448511_j_cmam-2025-0061_ref_007
2025091821510448511_j_cmam-2025-0061_ref_029
2025091821510448511_j_cmam-2025-0061_ref_006
2025091821510448511_j_cmam-2025-0061_ref_028
2025091821510448511_j_cmam-2025-0061_ref_005
2025091821510448511_j_cmam-2025-0061_ref_027
2025091821510448511_j_cmam-2025-0061_ref_004
2025091821510448511_j_cmam-2025-0061_ref_026
2025091821510448511_j_cmam-2025-0061_ref_021
2025091821510448511_j_cmam-2025-0061_ref_020
2025091821510448511_j_cmam-2025-0061_ref_040
2025091821510448511_j_cmam-2025-0061_ref_019
2025091821510448511_j_cmam-2025-0061_ref_014
2025091821510448511_j_cmam-2025-0061_ref_036
2025091821510448511_j_cmam-2025-0061_ref_013
2025091821510448511_j_cmam-2025-0061_ref_035
2025091821510448511_j_cmam-2025-0061_ref_012
2025091821510448511_j_cmam-2025-0061_ref_034
2025091821510448511_j_cmam-2025-0061_ref_011
2025091821510448511_j_cmam-2025-0061_ref_033
2025091821510448511_j_cmam-2025-0061_ref_018
2025091821510448511_j_cmam-2025-0061_ref_017
2025091821510448511_j_cmam-2025-0061_ref_039
2025091821510448511_j_cmam-2025-0061_ref_016
2025091821510448511_j_cmam-2025-0061_ref_038
2025091821510448511_j_cmam-2025-0061_ref_015
2025091821510448511_j_cmam-2025-0061_ref_037
2025091821510448511_j_cmam-2025-0061_ref_010
2025091821510448511_j_cmam-2025-0061_ref_032
2025091821510448511_j_cmam-2025-0061_ref_031
2025091821510448511_j_cmam-2025-0061_ref_030
References_xml – ident: 2025091821510448511_j_cmam-2025-0061_ref_039
– ident: 2025091821510448511_j_cmam-2025-0061_ref_020
  doi: 10.1142/S0218202508002784
– ident: 2025091821510448511_j_cmam-2025-0061_ref_009
  doi: 10.2172/800993
– ident: 2025091821510448511_j_cmam-2025-0061_ref_008
  doi: 10.1007/978-0-387-70914-7
– ident: 2025091821510448511_j_cmam-2025-0061_ref_038
  doi: 10.1088/2057-1976/abd239
– ident: 2025091821510448511_j_cmam-2025-0061_ref_017
  doi: 10.1142/S021820251150014X
– ident: 2025091821510448511_j_cmam-2025-0061_ref_018
  doi: 10.1137/15M1051336
– ident: 2025091821510448511_j_cmam-2025-0061_ref_031
  doi: 10.1016/B978-0-12-386944-9.50023-6
– ident: 2025091821510448511_j_cmam-2025-0061_ref_024
  doi: 10.3934/krm.2012.5.485
– ident: 2025091821510448511_j_cmam-2025-0061_ref_034
  doi: 10.1016/j.jmaa.2013.04.063
– ident: 2025091821510448511_j_cmam-2025-0061_ref_010
  doi: 10.1103/RevModPhys.15.1
– ident: 2025091821510448511_j_cmam-2025-0061_ref_037
  doi: 10.1118/1.4905041
– ident: 2025091821510448511_j_cmam-2025-0061_ref_001
– ident: 2025091821510448511_j_cmam-2025-0061_ref_026
  doi: 10.1007/978-3-540-85369-5_5
– ident: 2025091821510448511_j_cmam-2025-0061_ref_036
  doi: 10.1118/1.4937933
– ident: 2025091821510448511_j_cmam-2025-0061_ref_011
– ident: 2025091821510448511_j_cmam-2025-0061_ref_019
  doi: 10.1142/S0218202510004386
– ident: 2025091821510448511_j_cmam-2025-0061_ref_004
  doi: 10.1016/j.jmaa.2022.126946
– ident: 2025091821510448511_j_cmam-2025-0061_ref_015
  doi: 10.1080/00411458708204307
– ident: 2025091821510448511_j_cmam-2025-0061_ref_012
  doi: 10.1137/1.9780898719208
– ident: 2025091821510448511_j_cmam-2025-0061_ref_032
  doi: 10.1142/S021820259200003X
– ident: 2025091821510448511_j_cmam-2025-0061_ref_006
  doi: 10.1088/1361-6560/acf4de
– ident: 2025091821510448511_j_cmam-2025-0061_ref_023
  doi: 10.1088/0031-9155/51/3/013
– ident: 2025091821510448511_j_cmam-2025-0061_ref_022
  doi: 10.1090/conm/586/11649
– ident: 2025091821510448511_j_cmam-2025-0061_ref_033
  doi: 10.1007/978-3-0348-0513-1
– ident: 2025091821510448511_j_cmam-2025-0061_ref_021
  doi: 10.1088/0031-9155/51/9/010
– ident: 2025091821510448511_j_cmam-2025-0061_ref_002
  doi: 10.1007/978-1-4612-1994-1
– ident: 2025091821510448511_j_cmam-2025-0061_ref_013
– ident: 2025091821510448511_j_cmam-2025-0061_ref_027
  doi: 10.1118/1.597920
– ident: 2025091821510448511_j_cmam-2025-0061_ref_003
  doi: 10.1017/CBO9780511618833
– ident: 2025091821510448511_j_cmam-2025-0061_ref_030
  doi: 10.1137/S0036142998344706
– ident: 2025091821510448511_j_cmam-2025-0061_ref_007
  doi: 10.1088/0031-9155/60/13/4963
– ident: 2025091821510448511_j_cmam-2025-0061_ref_029
  doi: 10.1007/978-3-662-25839-2_2
– ident: 2025091821510448511_j_cmam-2025-0061_ref_014
  doi: 10.24033/asens.1516
– ident: 2025091821510448511_j_cmam-2025-0061_ref_025
– ident: 2025091821510448511_j_cmam-2025-0061_ref_028
– ident: 2025091821510448511_j_cmam-2025-0061_ref_005
  doi: 10.1007/BF02165003
– ident: 2025091821510448511_j_cmam-2025-0061_ref_016
  doi: 10.1088/1361-6560/ab9efe
– ident: 2025091821510448511_j_cmam-2025-0061_ref_040
  doi: 10.1088/0031-9155/55/3/002
– ident: 2025091821510448511_j_cmam-2025-0061_ref_035
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