## Section: New Results

### Recurrence phenomenon for finite element grid based Vlasov solver

Participants : Michel Mehrenberger, Laurent Navoret, Thi Nhung Pham.

When using a grid based solver (finite element/DG scheme, discontinuous Galerkin semi-Lagrangian scheme) and spatial periodic boundary conditions, the simulations of the Vlasov-Poisson system exhibit numerical reappearance of initial perturbations at some time called recurrence time. This time depends on the numerical parameters (degree and mesh size of the finite element mesh). With a given number of degrees of freedom, considering a large degree approximation makes the phenomenon appear earlier in the simulation and thus makes this choice less attractive. In our work [9], we highlight that the time and the intensity of the recurrence are related to the quadrature rules used for computing the charge density. In particular, quadratures that are exact on trigonometric polynomials weaken the recurrence effect.