no. 3
Numerical precision for differential inclusions with uniqueness
ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 3, pp. 427-460.

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.

DOI : 10.1051/m2an:2002020
Classification : 34A60, 34G25, 34K28, 47H05, 47J35, 65L70
Mots clés : differential inclusions, existence and uniqueness, multivalued maximal monotone operator, sub-differential, numerical analysis, implicit Euler numerical scheme, frictions laws 
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     title = {Numerical precision for differential inclusions with uniqueness},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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     publisher = {EDP-Sciences},
     volume = {36},
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Bastien, Jérôme; Schatzman, Michelle. Numerical precision for differential inclusions with uniqueness. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 3, pp. 427-460. doi : 10.1051/m2an:2002020. http://www.numdam.org/articles/10.1051/m2an:2002020/

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