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.
Bosboom et al. (Tue,) studied this question.