We consider one-dimensional steady-state balance laws with discontinuous
solutions. Giles and Pierce realized that a shock leads to a new term in the
adjoint error representation for target functionals.This term disappears if and
only if the adjoint solution satisfies an internal boundary condition.
Curiously, most computer codes implementing adjoint error estimation ignore the
new term in the functional, as well as the internal adjoint boundary condition.
The purpose of this note is to justify this omission as follows: if one
represents the exact forward and adjoint solutions as vanishing viscosity
limits of the corresponding viscous problems, then the internal boundary
condition is naturally satisfied in the limit
