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Numerical precision for differential inclusions with uniqueness

Published online by Cambridge University Press:  15 August 2002

Jérôme Bastien  and
Michelle Schatzman
Jérôme Bastien
Affiliation:
UMR 5585 CNRS, MAPLY, Laboratoire de mathématiques appliquées de Lyon, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France. jerome.bastien@utbm.fr. Laboratoire Mécatronique 3M, Université de Technologie de Belfort-Montbéliard, 90010 Belfort Cedex, France.
Michelle Schatzman
Affiliation:
UMR 5585 CNRS, MAPLY, Laboratoire de mathématiques appliquées de Lyon, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France.
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Abstract

In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is 1/2 in general and 1 when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl's rheological model, our estimates in maximum norm do not depend on spatial dimension.

Keywords

Differential inclusionsexistence and uniquenessmultivalued maximal monotone operatorsub-differentialnumerical analysisimplicit Euler numerical schemefrictions laws.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 3 , May 2002 , pp. 427 - 460
Copyright
© EDP Sciences, SMAI, 2002

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References

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