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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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FROM DISCRETE SYSTEMS TO INTEGRAL FUNCTIONALS

FROM DISCRETE SYSTEMS TO INTEGRAL FUNCTIONALS

Chapter:
(p.76) 4 FROM DISCRETE SYSTEMS TO INTEGRAL FUNCTIONALS
Source:
Gamma-Convergence for Beginners
Author(s):

Andrea Braides

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507840.003.0005

In this chapter, discrete systems and finite-difference schemes are interpreted as constrained variational problems, and are studied within the theory of Gamma-convergence for integral functionals to obtain a continuous limit integral energy. It is shown that for next-to-nearest neighbour interactions, this type of energies exhibit a multiple-scale behaviour mixing microscopic and mesoscopic oscillations.

Keywords:   finite-difference schemes, nearest-neighbour interactions, multiple scale phenomena, macroscopic oscillations

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