Section: New Results

Spline Discrete Differential Forms and applications

Participant : E. Sonnendrücker.

In [36] we construct a new set of discrete differential forms based on B-splines of arbitrary degree as well as an associated Hodge operator. The theory is first developed in 1D and then extended to multi-dimension using tensor products. We link our discrete differential forms with the theory of chains and cochains. The spline discrete differential forms are then applied to the numerical solution of Maxwell's equations.

The notion of B-spline based discrete differential forms is recalled and along with a Finite Element Hodge operator, it is used in [35] to design new numerical methods for solving the Vlasov-Poisson equations.