Convergence order of implicit Euler numerical scheme for maximal monotone differential inclusions



In the present work, we deal with the convergence of a class of numerical schemes for maximal monotone evolution systems in the particular case where the maximal monotone term is a subdifferential of a convex proper and lower semi-continuous function and the right-hand side depends on time and on solution. More precisely, we focus on an implicit Euler scheme and we show that the order of this scheme is one. Finally, some applications are given for a large class of rheological models.

Mathematics Subject Classification (2010)

Primary 34G25 Secondary 34A60 34K28 47H05 47J35 65L70 


Differential inclusions Implicit Euler numerical scheme Order one of convergence Multivalued maximal monotone operator Subdifferential Frictions laws 


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© Springer Basel 2012

Authors and Affiliations

  1. 1.Centre de Recherche et d’Innovation sur le Sport (CRIS), U.F.R.S.T.A.P.S.Université Claude Bernard-Lyon 1Villeurbanne CedexFrance

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