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An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional
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Burke, Siobhan, Ortner, Christoph and Süli, Endre (2013) An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional. Mathematical Models and Methods in Applied Sciences, Volume 23 (Number 9). pp. 1663-1697. doi:10.1142/S021820251350019X ISSN 0218-2025.
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Official URL: http://dx.doi.org/10.1142/S021820251350019X
Abstract
The Francfort–Marigo model of brittle fracture is posed in terms of the minimization of a highly irregular energy functional. A successful method for discretizing the model is to work with an approximation of the energy. In this work a generalized Ambrosio–Tortorelli functional is used. This leads to a bound-constrained minimization problem, which can be posed in terms of a variational inequality. We propose, analyze and implement an adaptive finite element method for computing (local) minimizers of the generalized functional.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Finite element method, Brittleness -- Mathematical models, Fracture mechanics | ||||||||
Journal or Publication Title: | Mathematical Models and Methods in Applied Sciences | ||||||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||||
ISSN: | 0218-2025 | ||||||||
Official Date: | 18 February 2013 | ||||||||
Dates: |
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Volume: | Volume 23 | ||||||||
Number: | Number 9 | ||||||||
Page Range: | pp. 1663-1697 | ||||||||
DOI: | 10.1142/S021820251350019X | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 27 December 2015 | ||||||||
Date of first compliant Open Access: | 27 December 2015 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
Grant number: | EP/E035027/1 (EPSRC) |
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