On the other hand, the EDG methods are no longer locally conservative. In the EDG methods, the numerical trace is taken to be continuous on a suitable collection of faces, thus resulting in an even smaller number of globally coupled degrees of freedom than in the HDG method. The EDG methods are thus obtained from the hybridizable discontinuous Galerkin (HDG) method by requiring the approximate trace to belong to smaller approximation spaces than the one in the HDG method. The essential ingredients are a local Galerkin projection of the underlying governing equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the approximate trace, a judicious choice of the numerical flux to provide stability and consistency, and a global jump condition that weakly enforces the single-valuedness of the numerical flux to arrive at a global formulation in terms of the numerical trace. We present a class of embedded discontinuous Galerkin (EDG) methods for numerically solving the Euler equations and the Navier–Stokes equations.
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