  We present a novel family of particle discretisation methods for the
nonlinear Landau collision operator. We exploit the metriplectic structure
underlying the Vlasov-Maxwell-Landau system in order to obtain disretisation
schemes that automatically preserve mass, momentum, and energy, warrant
monotonic dissipation of entropy, and are thus guaranteed to respect the laws
of thermodynamics. In contrast to recent works that used radial basis functions
and similar methods for regularisation, here we use an auxiliary spline or
finite element representation of the distribution function to this end.
Discrete gradient methods are employed to guarantee the aforementioned
properties in the time discrete domain as well.
