  The under integration of the volume terms in the discontinuous Galerkin
spectral element approximation introduces errors at non-conforming element
faces that do not cancel and lead to free-stream preservation errors. We derive
volume and face conditions on the geometry under which a constant state is
preserved. From those, we catalog six special cases on the geometry that
preserve a constant state, the most general being to approximate the geometry
sub-parametrically to one half the order of the solution. Numerical examples
are presented to illustrate the results.
