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

In: Approximation and Computation

Author

Listed:
  • Siobhan Burke

    (Mathematical Institute)

  • Christoph Ortner

    (Mathematical Institute)

  • Endre Süli

    (Mathematical Institute)

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.

Suggested Citation

  • Siobhan Burke & Christoph Ortner & Endre Süli, 2010. "Adaptive Finite Element Approximation of the Francfort–Marigo Model of Brittle Fracture," Springer Optimization and Its Applications, in: Walter Gautschi & Giuseppe Mastroianni & Themistocles M. Rassias (ed.), Approximation and Computation, pages 297-310, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-6594-3_19
    DOI: 10.1007/978-1-4419-6594-3_19
    as

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