Abstract
Conservatives and entropy schemes for the Fokker--Planck--Landau (FPL) equation are studied. We prove the existence of a unique positive and global in time solution for the homogeneous linear and nonlinear discretized (either in the velocity space or both in the velocity space and in time) FPL equation. The stability analysis of these schemes leads to sufficient conditions on the time-step that guarantee positivity and entropy decay.
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