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The problem of hydraulic fracture propagation is considered by using itsrecently suggested modified formulation in terms of the particle velocity, theopening in the proper degree, appropriate spatial coordinates and$\varepsilon$-regularization. We show that the formulation may serve forsignificant increasing the efficiency of numerical tracing the fracturepropagation. Its advantages are illustrated by re-visiting the Nordgrenproblem. It is shown that the modified formulation facilitates (i) possibilityto have various stiffness of differential equations resulting after spatialdiscretization, (ii) obtaining highly accurate and stable numerical resultswith moderate computational effort, and (iii) sensitivity analysis. Theexposition is extensively illustrated by numerical examples.

On modeling hydraulic fracture in proper variables: stiffness, accuracy, sensitivity