# Numerical precision for differential inclusions with uniqueness

Jérôme Bastien; Michelle Schatzman

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topBastien, Jérôme, and Schatzman, Michelle. "Numerical precision for differential inclusions with uniqueness." ESAIM: Mathematical Modelling and Numerical Analysis 36.3 (2010): 427-460. <http://eudml.org/doc/194111>.

@article{Bastien2010,

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},

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},

month = {3},

number = {3},

pages = {427-460},

publisher = {EDP Sciences},

title = {Numerical precision for differential inclusions with uniqueness},

url = {http://eudml.org/doc/194111},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Bastien, Jérôme

AU - Schatzman, Michelle

TI - Numerical precision for differential inclusions with uniqueness

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

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/194111

ER -

## References

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