Convergence of Lowest Order Semi-Lagrangian Schemes - Heumann, Holger; Hiptmair, Ralf (Foundations of computational mathematics, 2013)
We consider generalized linear transient advection-diffusion problems for differential forms on a bounded domain in ℝ d . We provide comprehensive a priori convergence estimates for their spatiotemporal discretization by means of a first-order in time semi-Lagrangian approach combined with a discontinuous Galerkin method. Under rather weak assumptions on the velocity underlying the advection we establish an asymptotic L 2 -estimate of order , where h is the spatial meshwidth, τ denotes the time step, and r is the polynomial degree of the forms used as trial functions. This estimate can be improved considerably in a variety of special settings.