  Numerical solutions to the adjoint Euler equations have been found to diverge
with mesh refinement near walls for a variety of flow conditions and geometry
configurations. The issue is reviewed and an explanation is provided by
comparing a numerical incompressible adjoint solution with an analytic adjoint
solution, showing that the anomaly observed in numerical computations is caused
by a divergence of the analytic solution at the wall. The singularity causing
this divergence is of the same type as the well-known singularity along the
incoming stagnation streamline and both originate at the adjoint singularity at
the trailing edge. The argument is extended to cover the fully compressible
case, in subcritical flow conditions, by presenting an analytic solution that
follows the same structure as the incompressible one.
