In the present work we present some results of numerical experiments obtained with a variational
model for quasi-static Griffith-type brittle fracture. Essentially the analysis is based on a recent formulation by
Francfort and Marigo the main difference being the fact that we rely on local rather than on global
minimization. Propagation of fracture is obtained by minimizing, in a step by step process, a form of energy
that is the sum of bulk and interface terms. To solve the problem numerically we adopt discontinuous finite
elements based on variable meshes and search for the minima of the energy through descent methods. We use a
sort of mesh dependent relaxation of the interface energy to get out of small energy wells. The relaxation
consists in the adoption of a carefully tailored cohesive type interface energy, tending to the Griffith limit as the
mesh size tends to zero.