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 notnecessarily included into V. We give a series of realisticconditions on an error estimator that allows to conclude that themarking strategy of bulk type leads to the geometric convergenceof the adaptive algorithm. These conditions are then verified fordifferent concrete problems like convection-reaction-diffusionproblems approximated by a discontinuous Galerkin methodwith an estimator of residual type or obtained by equilibratedfluxes. Numerical tests that confirm the geometric convergence arepresented.
