Convergence analysis of asymptotic preserving schemes for strongly magnetized plasmas

The present paper is devoted to the convergence analysis of a class asymptotic preserving particle schemes (Filbet and Rodrigues in SIAM J. Numer. Anal. 54(2):1120–1146, 2016) for Vlasov equation with strong external magnetic field. In this regime, classical Particle-in-Cell methods are subject quite restrictive stability constraints on time space steps, due small Larmor radius plasma frequency. discretization that we going study removes such constraint while capturing large-scale dynamics, even when (in space) too coarse capture fastest scales. Our error bounds explicit regarding discretization, stiffness parameter, initial data time.