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.
@article{arxiv.1809.05206,
title = {Free-Stream Preservation for Curved Geometrically Non-Conforming Discontinuous Galerkin Spectral Elements},
author = {David A. Kopriva and Florian Hindenlang and Thomas Boleman and Gregor J. Gassner},
journal= {arXiv preprint arXiv:1809.05206},
year = {2019}
}