The cohesive element approach is getting increasingly popular for simulations in which a large amount of cracking occurs. Naturally, a robust representation of fragmentation mechanics is contingent to an accurate description of dissipative mechanisms in form of cracking and branching. This paper addresses the issue of energy convergence of the finite-element solution for high-loading rate fragmentation problems. These results provide new insight for choosing mesh sizes and size distributions in two and three-dimensional fragmentation.