Moment Methods for the Semiconductor Boltzmann Equation on Bounded Position Domains

Galerkin methods for the semiconductor Boltzmann equation based on moment expansions for a discretization in the velocity direction are studied. For the moment equations, boundary conditions are proposed, which are analogues to inflow and, respectively, reflecting boundary conditions for the Boltzmann equation. Stability and an error estimate are proved for an expansion in terms of Hermite polynomials. Finally, an adaptive numerical implementation is introduced and results of numerical experiments are presented.