Stability and convergence of in time approximations of hyperbolic elastodynamics via stepwise minimization
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10492772" target="_blank" >RIV/00216208:11320/25:10492772 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=RPyljGWGqZ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=RPyljGWGqZ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2024.09.034" target="_blank" >10.1016/j.jde.2024.09.034</a>
Alternative languages
Result language
angličtina
Original language name
Stability and convergence of in time approximations of hyperbolic elastodynamics via stepwise minimization
Original language description
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much larger) for acceleration. The main applications are from elastodynamics, namely so-called generalized solids, undergoing large deformations. The evolution follows an underlying variational structure exploited by step-wise minimization. We show for a large family of (elastic) energies that the introduced scheme is stable; allowing for non-linearities of highest order. If the highest order can be assumed to be linear, we show that the limit solutions are regular and that the minimizing movements scheme converges with optimal linear rate. Thus this work extends numerical time-step minimization methods to the realm of hyperbolic problems.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Differential Equations
ISSN
0022-0396
e-ISSN
1090-2732
Volume of the periodical
415
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
53
Pages from-to
434-486
UT code for WoS article
001324593600001
EID of the result in the Scopus database
2-s2.0-85204617605