An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture.
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 two adaptive finite element algorithms for the computation of its (local) minimizers. For each algorithm, we combine a Newton-type method with residual-driven adaptive mesh refinement. We present two theoretical results which demonstrate convergence of our algorithms to local minimizers of the Ambrosio-To...Expand abstract
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