An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture.

Journal article

The energy of the Francfort-Marigo model of brittle fracture can be approximated, in the sense of Γ-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. © 2010 Society for Industrial and Applied Mathematics.

Authors: Burke, S; Ortner, C; Süli, E

• Publication status: Published
• Journal: SIAM J. Numerical Analysis
• Volume: 48
• Issue: 3
• Pages: 980-1012
• Publication date: 2010-01-01
• DOI: 10.1137/080741033
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: adaptive finite element method; brittle fracture; Ambrosio-Tortorelli functional; free-discontinuity problem