  We present a hybrid continuous and discontinuous Galerkin spectral element
approximation that leverages the advantages of each approach. The continuous
Galerkin approximation is used on interior element faces where the equation
properties are continuous. A discontinuous Galerkin approximation is used at
physical boundaries and if there is a jump in properties at a face. The
approximation uses a split form of the equations and two-point fluxes to ensure
stability for unstructured quadrilateral/hexahedral meshes with curved
elements. The approximation is also conservative and constant state preserving
on such meshes. Spectral accuracy is obtained for all examples, which include
wave scattering at a discontinuous medium boundary.
