Recurrence phenomenon for Vlasov-Poisson simulations on regular finite element mesh

In this paper, we focus on one difficulty arising in the numerical simulationof the Vlasov-Poisson system: when using a regular grid-based solver with periodicboundary conditions, perturbations present at the initial time artificially reappear at alater time. For regular finite-element mesh in velocity, we show that this recurrence timeis actually linked to the spectral accuracy of the velocity quadrature when computingthe charge density. In particular, choosing trigonometric quadrature weights optimallydefers the occurence of the recurrence phenomenon. Numerical results using the Semi-Lagrangian Discontinuous Galerkin and the Finite Element / Semi-Lagrangian methodconfirm the analysis