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An adaptive finite element approximation of a generalised ambrosio–tortorelli functional
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Burke, Siobhan, Ortner, Christoph and Süli, Endre (2010) An adaptive finite element approximation of a generalised ambrosio–tortorelli functional. Working Paper. Oxford: Mathematical Institute, University of Oxford. OxMOS Preprint Series (No.29). (Unpublished)
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Official URL: http://www2.maths.ox.ac.uk/oxmos/reports/pdfs/oxmo...
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 generalised 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, analyse and implement an adaptive finite element method for computing (local) minimizers of the generalised functional.
Item Type: | Working or Discussion Paper (Working Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Series Name: | OxMOS Preprint Series | ||||
Publisher: | Mathematical Institute, University of Oxford | ||||
Place of Publication: | Oxford | ||||
Official Date: | 2010 | ||||
Dates: |
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Number: | No.29 | ||||
Number of Pages: | 51 | ||||
Status: | Not Peer Reviewed | ||||
Publication Status: | Unpublished | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
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