Implicit level set schemes for modeling hydraulic fractures using the XFEM

We describe two novel XFEM schemes for modeling fluid driven fractures both of which exploit an implicit level set algorithm (ILSA) for locating the singular free boundary that occurs when the fluid and fracture fronts coalesce. Both schemes use the mixed PW Garagash and Detournay, 2000 [4]). The two ILSA-XFEM schemes differ in the enrichment strategies that they use to represent the fracture tips: a scheme with full tip enrichment and a simpler, more efficient, scheme in which the tip asymptotic behavior is only imposed in a weak sense. Numerical experiments indicate that the XFEM-t scheme, with full tip enrichment, achieves an Oðh 2 Þ asymptotic convergence rate, while the XFEM-s scheme, with only signum enrichment

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