  The main result in this paper is a provably entropy stable shock capturing
approach for the high order entropy stable DGSEM based on a hybrid blending
with a subcell low order variant. Since it is possible to rewrite a high order
SBP operator into an equivalent conservative finite volume form, we were able
to design a low order scheme directly with the LGL nodes that is compatible to
the discrete entropy analysis used for the proof of the entropy stable DGSEM.
Furthermore, we present a hybrid low order/high order discretisation where it
is possible to seamlessly blend between the two approaches, while still being
provably entropy stable. We are able to extend the approach to three spatial
dimensions on unstructured curvilinear hexahedral meshes. We validate our
theoretical findings and demonstrate convergence order for smooth problems,
conservation of the primary quantities and discrete entropy stability for an
arbitrary blending on curvilinear grids. In practical simulations, we connect
the blending factor to a local troubled element indicator that provides the
control of the amount of low order dissipation injected into the high order
scheme. We modified an existing shock indicator, which is based on the modal
polynomial representation, to our provably stable hybrid scheme. The aim is to
reduce the impact of the parameters as good as possible. We describe our
indicator in detail and demonstrate its robustness in combination with the
hybrid scheme, as it is possible to compute all the different test cases
without changing the indicator. The test cases include e.g. the double Mach
reflection setup, forward and backward facing steps with shock Mach numbers up
to 100. The proposed approach is relatively straight forward to implement in an
existing entropy stable DGSEM code as only modifications local to an element
are necessary.
