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Adaptive finite element approximation of the Francfort–Marigo model of brittle fracture
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Burke, Siobhan, Ortner, Christoph and Süli, Endre (2010) Adaptive finite element approximation of the Francfort–Marigo model of brittle fracture. In: Gautschi, Walter and Mastroianni, Giuseppe and Rassias, Themistocles M., (eds.) Approximation and Computation. Springer optimization and its applications, Vol.42 . New York: Springer, pp. 297-310. ISBN 9781441965943
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Official URL: http://dx.doi.org/10.1007/978-1-4419-6594-3_19
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.
Item Type: | Book Item | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Series Name: | Springer optimization and its applications | ||||
Publisher: | Springer | ||||
Place of Publication: | New York | ||||
ISBN: | 9781441965943 | ||||
ISSN: | 1931-6828 | ||||
Book Title: | Approximation and Computation | ||||
Editor: | Gautschi, Walter and Mastroianni, Giuseppe and Rassias, Themistocles M. | ||||
Official Date: | 2010 | ||||
Dates: |
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Volume: | Vol.42 | ||||
Number of Pages: | 480 | ||||
Page Range: | pp. 297-310 | ||||
DOI: | 10.1007/978-1-4419-6594-3_19 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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