On the moving boundary conditions for a hydraulic fracture

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Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm (2015, background): “For a permeable medium, this limit can be finite or tend to infinity depending on the tip asymptote [22].”
Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems (2015, background): “Given the fact that the pressure is singular at the crack tip when the fluid and the fracture fronts coalesce [39], an iterative solution for the pressure is likely to be inaccurate at the nodes very close to the crack tip.”
Phase-field modeling of hydraulic fracture (2016, background): “Detournay has revisited this problem, as well as a few other simple geometries like the penny-shaped crack, and conducted state-of-the-art analytical and numerical studies([15-17,86]).”
Hydraulic fracture revisited: Particle velocity based simulation (2015, methodology): “In the numerical scheme proposed in Sections 5 and 6 below, we use a strategy for finding the fracture tip different from that advocated in Detournay and Peirce (2014).”