|Abstract:|| In this work we introduce a fully computable
dual-based a posteriori error estimator for
standard scalar advection-diffusion-reaction
problems. In particular, such an estimator does not depend
on neither the primal nor the dual exact solution, but only on the
corresponding Galerkin finite element approximations.
This new approach merges the main advantages of the dual-based and of the
residual-based error analysis, being devised as a residual-based estimator
nested in a dual-based one.
This allows us to explicitly approximate suitable functionals of
the solution, in the spirit of a classical goal-oriented analysis,
at the same cost as a dual-based strategy, the solution of two
differential problems being involved.
The related issue of optimal mesh adaptivity is also addressed.
Several two-dimensional numerical test cases validate the proposed theory
as well as the employed adaptive procedure.|