  In the discretization of differential problems on complex geometrical
domains, discretization methods based on polygonal and polyhedral elements are
powerful tools. Adaptive mesh refinement for such kind of problems is very
useful as well and states new issues, here tackled, concerning good quality
mesh elements and reliability of the simulations. In this paper we numerically
investigate optimality with respect to the number of degrees of freedom of the
numerical solutions obtained by the different refinement strategies proposed. A
geometrically complex geophysical problem is used as test problem for several
general purpose and problem dependent refinement strategies.
