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

Siobhan Burke (), Christoph Ortner () and Endre Süli ()
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Siobhan Burke: Mathematical Institute
Christoph Ortner: Mathematical Institute
Endre Süli: Mathematical Institute

A chapter in Approximation and Computation, 2010, pp 297-310 from Springer

Abstract: Abstract 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.

Keywords: Brittle Fracture; Crack Path; Adaptive Finite Element; Inexact Newton Method; Energy Minimization Problem (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-6594-3_19

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DOI: 10.1007/978-1-4419-6594-3_19

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