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A Γ-convergence result for variational integrators of lagrangians with quadratic growth

Published online by Cambridge University Press:  15 October 2004

Francesco Maggi  and
Massimiliano Morini
Francesco Maggi
Affiliation:
Dipartimento di Matematica “U. Dini”, Viale Morgagni 67/A 50134, Firenze, Italy.
Massimiliano Morini
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA, 15213 USA; morini@asdf4.math.cmu.edu.
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Abstract

Following the Γ-convergence approach introduced by Müller and Ortiz, the convergence of discrete dynamics for Lagrangians with quadratic behavior is established.

Keywords

Discrete dynamicsvariational integratorsGamma-convergence.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 4 , October 2004 , pp. 656 - 665
Copyright
© EDP Sciences, SMAI, 2004

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References

E. De Giorgi, Teoremi di semicontinuitá nel Calcolo delle Variazioni. Istituto Nazionale di Alta Matematica (1968-1969).
Ioffe, A.D., On lower semicontinuity of integral functionals. I. SIAM J. Control Optim. 15 (1977) 521-538. CrossRef
Marsden, E.J. and West, M., Discrete Mechanics and variational integrators. Acta Numerica 10 (2001) 357-514. CrossRef
Müller, S. and Ortiz, M., On the $\Gamma$ -convergence of discrete dynamics and variational integrators. J. Nonlinear Sci. 14 (2004) 279-296. CrossRef