M. Lemou, THE AXISYMMETRICAL FOKKER-PLANCK-LANDAU O PERATOR, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 326(2), 1998, pp. 179-184
We establish a simplified form of the axisymmetric Fokker-Planck-Landa
u operator (in the velocity space). In doing so, we derive a weak form
ulation of this operator on which we get directly the conservation pro
perties and the decay of the entropy as it is the case for the full th
ree-dimensional operator (see [1]). A symmetrized version of this form
ulation leads to a class of numerical schemes which satisfy these phys
ical properties at the discrete level.