Numerical integration of the nonlinear Klein-Gordon equations at low regularity and conservation properties (Joackim Bernier (Nantes Université)

19.12.2023 14:00

Close to the origin, the nonlinear Klein--Gordon equations on the circle are nearly integrable Hamiltonian systems which have infinitely many almost conserved quantities called "harmonic energies" or "super-actions". In a series of works in 2008,  D. Cohen, E. Hairer and C. Lubich proved that, at high regularity, classical symplectic numerical integrators preserve this qualitative property (even if the CFL number is not small).  I will present a joint work with C. Abou Khalil (in progress), in which we extend this result for non-smooth solutions.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

entrée libre