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Approximation and Computation pp 297–310Cite as

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

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

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.

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Authors and Affiliations

  1. Mathematical Institute, 24–29 St. Giles’, Oxford, OX1 3LB, UK

    Siobhan Burke, Christoph Ortner & Endre Süli

Authors
  1. Siobhan Burke
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  2. Christoph Ortner
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  3. Endre Süli
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Corresponding author

Correspondence to Siobhan Burke .

Editor information

Editors and Affiliations

  1. Dept. Computer Science, Purdue University, N. University Street 305, West Lafayette, 47907-2107, Indiana, USA

    Walter Gautschi

  2. Dipto. Matematica, Università Basilicata, Contrada Macchia Romana, Potenza, 85100, Italy

    Giuseppe Mastroianni

  3. Zagoras Street 4, Athens, 151 25, Greece

    Themistocles M. Rassias

Additional information

Dedicated to Gradimir V. Milovanović on his 60th birthday

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Burke, S., Ortner, C., Süli, E. (2010). Adaptive Finite Element Approximation of the Francfort–Marigo Model of Brittle Fracture. In: Gautschi, W., Mastroianni, G., Rassias, T. (eds) Approximation and Computation. Springer Optimization and Its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6594-3_19

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