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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