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We consider one-dimensional steady-state balance laws with discontinuoussolutions. Giles and Pierce realized that a shock leads to a new term in theadjoint error representation for target functionals.This term disappears if andonly if the adjoint solution satisfies an internal boundary condition.Curiously, most computer codes implementing adjoint error estimation ignore thenew 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 onerepresents the exact forward and adjoint solutions as vanishing viscositylimits of the corresponding viscous problems, then the internal boundarycondition is naturally satisfied in the limit.

A note on adjoint error estimation for one-dimensional stationary balance laws with shocks