Numerical precision for differential inclusions with uniqueness
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 3, p. 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 : https://doi.org/10.1051/m2an:2002020
Classification:  34A60,  34G25,  34K28,  47H05,  47J35,  65L70
Keywords: differential inclusions, existence and uniqueness, multivalued maximal monotone operator, sub-differential, numerical analysis, implicit Euler numerical scheme, frictions laws
@article{M2AN_2002__36_3_427_0,
     author = {Bastien, J\'er\^ome and Schatzman, Michelle},
     title = {Numerical precision for differential inclusions with uniqueness},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {3},
     year = {2002},
     pages = {427-460},
     doi = {10.1051/m2an:2002020},
     zbl = {1036.34012},
     mrnumber = {1918939},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2002__36_3_427_0}
}
Bastien, Jérôme; Schatzman, Michelle. Numerical precision for differential inclusions with uniqueness. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 3, pp. 427-460. doi : 10.1051/m2an:2002020. http://www.numdam.org/item/M2AN_2002__36_3_427_0/

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