Recent analytic progress has increased demand for numerical approaches to the Wigner-Fokker-Planck (WFP) equation. We present a Discontinuous Galerkin scheme for the WFP equation with a general potential. Estimates showing stability of the scheme are provided. The scheme is convergence and adaptable, and may use both polynomial and non-polynomial basis functions.
"An adaptable discontinuous Galerkin scheme for the Wigner-Fokker-Planck equation." Commun. Math. Sci. 7 (3) 635 - 664, September 2009.