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An adaptive finite element approximation of a generalised Ambrosio–Tortorelli functional

By S. Burke, C. Ortner and E. Süli

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

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.185.3015
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