A MICRO-MACRO METHOD FOR A KINETIC GRAPHENE MODEL IN ONE SPACE DIMENSION

In this paper, we propose a numerical method solving the one space dimensional semiclassical kinetic graphene model introduced in [O. Morandi and F. Schurrer, T. Phys. A, 44 (2012), pp. 265-301] involving fast oscillations in time, space, and momentum. This method can numerically capture the oscillatory space-time quantum solution pointwisely even without numerically resolving the frequency. We prove that the underlying micro-macro equations have smooth (up to a certain order of derivatives) solutions with respect to the frequency, and then we prove the uniform accuracy of the numerical discretization for a scalar model equation exhibiting the same oscillatory behavior. Numerical experiments verify the theory.