  A discrete analysis of the phase and dissipation errors of an explicit,
semi-Lagrangian spectral element method is performed. The semi-Lagrangian
method advects the Lagrange interpolant according the Lagrangian form of the
transport equations and uses a least-square fit to correct the update for
interface constraints of neighbouring elements. By assuming a monomial
representation instead of the Lagrange form, a discrete version of the
algorithm on a single element is derived. The resulting algebraic system lends
itself to both a Modified Equation analysis and an eigenvalue analysis. The
Modified Equation analysis, which Taylor expands the stencil at a single space
location and time instance, shows that the semi-Lagrangian method is consistent
with the PDE form of the transport equation in the limit that the element size
goes to zero. The leading order truncation term of the Modified Equation is of
the order of the degree of the interpolant which is consistent with numerical
tests reported in the literature. The dispersion relations show that the method
is negligibly dispersive, as is common for semi-Lagrangian methods. An
eigenvalue analysis shows that the semi-Lagrangian method with a nodal
Chebyshev interpolant is stable for a Courant-Friedrichs-Lewy condition based
on the minimum collocation node spacing within an element that is greater than
unity.
