Titre: Energy consistent time discretisation of port-Hamiltonian systems
Résumé
Various ordinary and partial differential equations arising from physics can be written as port-Hamiltonian systems. Their Hamiltonian function represents an energy that is conserved or dissipated along solutions.
Numerical schemes are energy consistent, if the Hamiltonian is preserved or dissipated also along the approximate solutions. This type of structure preservation is not in general satisfied by standard continuous Petrov-Galerkin (cPG) methods in time of arbitrary order.
In this talk we present a modification of the cPG method of arbitrary order, which is energy consistent for a general class of port-Hamiltonian systems. If time permits I will outline how this approach extends to structure preserving space discretisation.
This is joint work with Jan Giesselmann (TU Darmstadt) and Attila Karsai (TU Berlin).
