Adaptive Finite Element Approximation of the Francfort–Marigo Model of Brittle Fracture

Part of the Springer Optimization and Its Applications book series (SOIA, volume 42)


The energy of the Francfort–Marigo model of brittle fracture can be approximated, in the sense of Γ-convergence, by the Ambrosio-Tortorelli functional. In this work we formulate and analyze an adaptive finite element algorithm, combining an inexact Newton method with residual-driven adaptive mesh refinement, for the computation of its (local) minimizers. We prove that the sequence generated by this algorithm converges to a critical point.


Brittle Fracture Crack Path Adaptive Finite Element Inexact Newton Method Energy Minimization Problem 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematical InstituteOxfordUK

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