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Gamma-Convergence for Beginners$
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Andrea Braides

Print publication date: 2002

Print ISBN-13: 9780198507840

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198507840.001.0001

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APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS

APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS

Chapter:
(p.121) 8 APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0009

Various types of approximations of free-discontinuity energies, in particular the Mumford-Shah functional, are given: the Ambrosio-Tortorelli approximation via elliptic functionals with an additional variable (interpreted as a damage parameter in a mechanical setting); convolution functionals (interpreted as non-local damage energies), in particular the Braides-Dal Maso approximation; and non-convex finite-difference schemes.

Keywords:   free-discontinuity, Mumford-Shah functional, Ambrosio-Tortorelli approximation, non-local approximation, non-convex finite-difference schemes

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