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