This may a broad field, and I hope that I don't muddy things by making this statement too broad: moving nodes in 8 or 9 noded quadrilaterals to the quarter point (from this midpoints of the edges), closer to the crack tip, often improves, sometimes substantially, the finite element solution and computation of engineering data such as stresses and Stress Intensity Factors. The reason is, I recall, that moving the nodes to the quarter points results in a coordinate mapping with functional form that closely matches the exact solution.