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An adaptive finite element approximation of a variational model of brittle fracture
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Burke, Siobhan, Ortner, Christoph and Süli, Endre (2010) An adaptive finite element approximation of a variational model of brittle fracture. SIAM Journal on Numerical Analysis, Volume 48 (Number 3). pp. 980-1012. doi:10.1137/080741033 ISSN 0036-1429.
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Official URL: http://dx.doi.org/10.1137/080741033
Abstract
The energy of the Francfort–Marigo model of brittle fracture can be approximated, in the sense of Gamma-convergence, by the Ambrosio–Tortorelli functional. In this work, we formulate and analyze two adaptive finite element algorithms for the computation of its (local) minimizers. For each algorithm, we combine a Newton-type method with residual-driven adaptive mesh refinement. We present two theoretical results which demonstrate convergence of our algorithms to local minimizers of the Ambrosio–Tortorelli 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, Fracture mechanics, Brittleness -- Mathematical models | ||||||||
Journal or Publication Title: | SIAM Journal on Numerical Analysis | ||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||
ISSN: | 0036-1429 | ||||||||
Official Date: | 1 July 2010 | ||||||||
Dates: |
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Volume: | Volume 48 | ||||||||
Number: | Number 3 | ||||||||
Page Range: | pp. 980-1012 | ||||||||
DOI: | 10.1137/080741033 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 20 December 2015 | ||||||||
Date of first compliant Open Access: | 20 December 2015 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
Adapted As: |
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