EULERIAN AND SEMI-LAGRANGIAN METHODS FOR CONVECTION-DIFFUSION FOR DIFFERENTIAL FORMS

We consider generalized linear transient convection-diffusion problems for differential forms on bounded domains in R-n. These involve Lie derivatives with respect to a prescribed smooth vector field. We construct both new Eulerian and semi-Lagrangian approaches to the discretization of the Lie derivatives in the context of a Galerkin approximation based on discrete differential forms. Our focus is on derivations of the schemes, details of implementation, as well as on application to the discretization of eddy current equations in moving media.