Title: On the Necessity of Superparametric Geometry Representation for Discontinuous Galerkin Methods on Domains with Curved Boundaries,
Abstract: We provide numerical evidence demonstrating the necessity of employing a
superparametric geometry representation in order to obtain optimal convergence
orders on two-dimensional domains with curved boundaries when solving the Euler
equations using Discontinuous Galerkin methods. However, concerning the
obtention of optimal convergence orders for the Navier-Stokes equations, we
demonstrate numerically that the use of isoparametric geometry representation
is sufficient for the case considered here.