Issue |
ESAIM: M2AN
Volume 36, Number 3, May/June 2002
|
|
---|---|---|
Page(s) | 427 - 460 | |
DOI | https://doi.org/10.1051/m2an:2002020 | |
Published online | 15 August 2002 |
Numerical precision for differential inclusions with uniqueness
1
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.
2
UMR 5585 CNRS, MAPLY,
Laboratoire de mathématiques appliquées de Lyon,
Université Claude
Bernard Lyon I,
69622 Villeurbanne Cedex, France.
Received:
18
December
2001
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.
Mathematics Subject Classification: 34A60 / 34G25 / 34K28 / 47H05 / 47J35 / 65L70
Key words: Differential inclusions / existence and uniqueness / multivalued maximal monotone operator / sub-differential / numerical analysis / implicit Euler numerical scheme / frictions laws.
© EDP Sciences, SMAI, 2002
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