The development of adaptive numerical schemes for steady transport
equations is addressed. A goal-oriented error estimator is presented
and used as a refinement criterion for conforming mesh adaptation. The
error in the value of a linear target functional is measured in terms
of weighted residuals that depend on the solutions to the primal and
dual problems. The Galerkin orthogonality error is taken into account
and found to be important whenever flux or slope limiters are activated
to enforce monotonicity constraints. The localization of global errors
is performed using a natural decomposition of the involved weights
into nodal contributions. A nodal generation function is employed in a
hierarchical mesh adaptation procedure which makes each refinement
step readily reversible. The developed simulation tools are applied to
a linear convection problem in two space dimensions.