Numerical precision for differential inclusions with uniqueness

Jérôme Bastien; Michelle Schatzman

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 3, page 427-460
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bastien, Jérôme, and Schatzman, Michelle. "Numerical precision for differential inclusions with uniqueness." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.3 (2002): 427-460. <http://eudml.org/doc/245686>.

@article{Bastien2002,
abstract = {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.},
author = {Bastien, Jérôme, Schatzman, Michelle},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {differential inclusions; existence and uniqueness; multivalued maximal monotone operator; sub-differential; numerical analysis; implicit Euler numerical scheme; frictions laws; Differential inclusion; maximal monotone evolution system; existence; uniqueness; numerical precision},
language = {eng},
number = {3},
pages = {427-460},
publisher = {EDP-Sciences},
title = {Numerical precision for differential inclusions with uniqueness},
url = {http://eudml.org/doc/245686},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Bastien, Jérôme
AU - Schatzman, Michelle
TI - Numerical precision for differential inclusions with uniqueness
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 3
SP - 427
EP - 460
AB - 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.
LA - eng
KW - differential inclusions; existence and uniqueness; multivalued maximal monotone operator; sub-differential; numerical analysis; implicit Euler numerical scheme; frictions laws; Differential inclusion; maximal monotone evolution system; existence; uniqueness; numerical precision
UR - http://eudml.org/doc/245686
ER -

References

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