We consider a general abstract framework of a continuous elliptic
problem set on a Hilbert space V that is approximated by a family of (discrete) problems
set on a finite-dimensional space of finite dimension not
necessarily included into V. We give a series of realistic
conditions on an error estimator that allows to conclude that the
marking strategy of bulk type leads to the geometric convergence
of the adaptive algorithm. These conditions are then verified for
different concrete problems like convection-reaction-diffusion
problems approximated by a discontinuous Galerkin method
with an estimator of residual type or obtained by equilibrated
fluxes. Numerical tests that confirm the geometric convergence are
presented.