“…12 The solution of the adjoint problem is the natural connection between the 13 linearisations of the residual and the considered objective functional. Con- 14 sequently, the adjoint system inherits all the potential inconsistencies lying 15 between the residual and the objective; either on the level of partial differen- 16 tial equations (PDE) when the continuous-adjoint problem is constructed in 17 a derive-then-discretise approach [14,15,25,28,26], or on the discrete level algebraic constraints (discretised governing equations) weighted by the cor-43 responding discrete-adjoint multipliers. Summation by parts, the discrete [5,7], Nielsen et al [20] have manually ensured primal-dual 57 equivalence throughout the iteration process of a linearised, unstructured 58 finite-volume Navier-Stokes method.…”