A phase field approach to pressurized fractures using discontinuous Galerkin methods

Subsurface fractures play an important role in many modern energy technologies (e.g. geothermal energy, fracking, nuclear waste management). Real world experiments concerning fracture propagation are usually expensive and time consuming, therefore numerical simulations become more and more important in this area. The main challenge for numerical methods is the evolving domain. Standard finite element (FE) methods require remeshing to resolve the crack surface once a fracture starts propagating. To overcome this problem we use a phase field approach to regularize the crack surface. Thereby we consider quasi static evolution in fluid filled media. For the one-dimensional case Γ-convergence of the approximating functional to the potential energy of the system is shown. Based on this model we propose a discontinuous Galerkin (DG) formulation for the displacement. This takes into account displacement jumps at the crack surface. Numerical experiments compare our method with a standard FE approach.