A robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures. This class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small-sized critical regions. The proposed approach is based on the division of a simulation into a suitable number of sub-simulations where adaptive mesh refinement is performed only once based on refinement window(s) around crack front process zone(s). The initialization of Newton-Raphson nonlinear iterations at the start of each sub-simulation is accomplished by solving a linear problem based on a secant stiffness, rather than a volume mapping of nonlinear solutions between meshes. The secant stiffness is evaluated using material state information stored/read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework. Moreover, a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software. Data transfer between sub-simulations is not required in the simplified strategy. The computational efficiency, accuracy, and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3-D.@en