Analysis of a Semidiscrete Version of the Wigner Equation
Thierry Goudon · SIAM Journal on Numerical Analysis · 2002
We introduce a semidiscretized version of the Wigner equation---discretization concerning the velocity variable. We show that the corresponding discrete velocity problem is well-posed and permits us to approach the solution of the continuous problem when the mesh size of the discretization vanishes. The approximation shows spectral accuracy because the rate of convergence corresponds to the (Sobolev) regularity of the solution of the continuous problem. We also discuss the behavior of the solution with respect to the Planck constant.