  We deal with the numerical solution of the compressible Euler equations with
the aid of the discontinuous Galerkin (DG) method with focus on the
goal-oriented error estimates and adaptivity. We analyze the adjoint
consistency of the DG scheme where the dual problem is not formulated by the
differentiation of the DG form and the target functional but using a suitable
linearization of the nonlinear forms. Further, we present the goal-oriented
anisotropic $hp$-mesh adaptation technique for the Euler equations. The
theoretical results are supported by numerical experiments.

Numerical Analysis;Numerical Analysis