  We propose a class of semi-Lagrangian methods of high approximation order in
space and time, based on spectral element space discretizations and exponential
integrators of Runge-Kutta type. We discuss the extension of these methods to
the Navier-Stokes equations, and their implementation using projections.
Semi-Lagrangian methods up to order three are implemented and tested on various
examples. The good performance of the methods for convection-dominated problems
is demonstrated with numerical experiments.
