Volume 36, Number 3, May/June 2002
|Page(s)||427 - 460|
|Published online||15 August 2002|
Numerical precision for differential inclusions with uniqueness
UMR 5585 CNRS, MAPLY,
Laboratoire de mathématiques appliquées de Lyon,
Bernard Lyon I,
69622 Villeurbanne Cedex, France. firstname.lastname@example.org.
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.
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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