Accurate determination of the coefficients of elastic crack tip asymptotic field

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Polygon scaled boundary finite elements for crack propagation modelling (2012, background): “Local mesh refinements, stress recovery techniques [10] or special finite elements, for example [11, 12] are often employed to accurately represent the singular stresses around the crack tip.”
Higher order terms of the crack tip asymptotic field for a notched three-point bend beam (2001, background): “ Karihaloo and Xiao (2001) showed that the accurate determination of the coefficients of higher order terms requires a higher order HCE together with a finer discretisation of the remainder of the body.”
A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics (2017, methodology): “Xiao and Karihaloo [25, 27, 39] employed a hybrid technique within the framework of the extended finite element method, thus facilitating the computation of stress intensity factors without additional post-processing.”
A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics (2011, background): “[6], while a more recent approach, known as the fractal finite element method (FFEM) [7] has been developed.”
A hybrid-Trefftz element containing an elliptic hole (2006, methodology): “Karihaloo and Xiao [2] have improved the superelements formulated in [1] by using the modified Hellinger–Reissner principle and hybrid element technique.”