The talk focuses on the convergence analysis of space-time discrete approximation schemes for a model for rate-independent crack propagation in an ideally brittle elastic body. The single crack is supposed to propagate along a prescribed crack path, and the Griffith fracture criterion serves as a basis for our modeling. Following ideas of Efendiev and Mielke (2006) and Knees and Shcherbakov (2021), we define the evolution of the crack by means of local minimizers of the total energy. The set of discretization parameters comprises the mesh size, crack increment, locality parameter, and regularization parameter. We present sufficient conditions on the discretization parameters that guarantee the convergence of discrete interpolants to parametrized balanced viscosity solutions of the continuous model. Finally, we provide numerical experiments demonstrating the convergence properties of the approximation schemes. This is a joint work with Dorothee Knees (University of Kassel) and Andreas Schröder (University of Salzburg).