The economic feasibility of the exploitation of unconventional oil and gas resources is enhanced when it is possible to analyze a priori, with a reasonable accuracy, the effects of different hydraulic fracturing schemes (different fracturing fluids, different proppant concentrations, etc.) and compare them with the results in terms of the predicted production, enabling therefore the selection of the optimal alternative. Two basic ingredients for these analyses are a reliable numerical technique and an adequate geomechanical characterization of the reservoir.
The use of the Discontinuous Galerkin Method (DGM) to simulate fracture processes is discussed, with the perspective of implementing this technique to simulate the hydraulic fracturing of shale formations. It is important to remark that resulting models capture the proper fracture mechanical physics required to model nucleation and propagation of fractures.
Two examples are discussed. First, the well-known Brazilian Test is modelled; in this case the dominant phenomenon is fracture nucleation. Second, a Brazilian Test including a slot is modelled, this is a typical fracture mechanics test used for studying fracture propagation in rocks.
The strong momentum that hydraulic fracturing processes  are attaining nowadays in the oil industry, for the exploitation of unconventional gas and oil reservoirs, encourages operating companies, oil service companies, software development companies and academic institutions to invest increasing resources in the research and development of hydraulic fracturing computational simulators.
There are many numerical methodologies for modeling fracture processes, each of them with their own advantages and limitations.