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An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional

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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1142/S021820251350019X

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
World Scientific Publisher's website
Journal:
Mathematical Models and Methods in Applied Sciences Journal website
Volume:
23
Issue:
9
Pages:
1663-1697
Publication date:
2013-01-01
DOI:
EISSN:
1793-6314
ISSN:
0218-2025
URN:
uuid:81c51687-297d-4c17-b335-8a99a42a399f
Source identifiers:
408085
Local pid:
pubs:408085

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