Whereas Griewank introduced a globalization strategy using a doubly augmented Lagrangian function that includes primal and adjoint residuals, its practical usability is limited by the necessity of second order derivatives and expensive line search iterations.
An adjoint formulation is used to relate the estimated functional error to the local residual errors of both the primal and adjoint solutions.
The procedure is based on an adjoint formulation in which the estimated error in the functional can be directly related to the local residual errors of both the primal and adjoint solutions.
Adaptive criteria are derived using an adjoint-based error correction technique that relates the local residual errors of both the primal and adjoint solutions to the global error in the prescribed functional.
Error estimates are computed using an adjoint-weighted residual, where the discrete adjoint is computed on a finer space obtained by order enrichment of the primal space.
The minimization of the energy of the primal problem as well as the minimization of the energy of the dual problem with respect to a design function lead to the primal and dual material residuals, respectively.
