We present a Discontinuous Galerkin scheme Wigner-Fokker-Planck (WFP)
equation. The scheme is adaptable to unstructured meshes in space an time, as well as order of approximation, and may use both polynomial and non-polynomial basis functions. Alternative approaches include splitting methods and iterative schemes based on Hermite expansions or Bloch functions, but are rather restricted to the shape of the potential function. Our scheme can be implemented fairly easy for perturbations of harmonic potentials, exhibiting a signature of quantum effects due to the dispersion effect from the equation. We also present preliminary stability and error estimates in suitable norms.
This is work in collaboration with Richard Sharp at Carnegie Mellon University, and Maria P. Gualdani at UT-Austin.