Regularity and approximation of strong solutions to rate-independent systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10372070" target="_blank" >RIV/00216208:11320/17:10372070 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S0218202517500518" target="_blank" >http://dx.doi.org/10.1142/S0218202517500518</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218202517500518" target="_blank" >10.1142/S0218202517500518</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Regularity and approximation of strong solutions to rate-independent systems

Popis výsledku v původním jazyce

Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this work, we prove the existence of Holder-regular strong solutions for a class of rate-independent systems. We also establish additional higher regularity results that guarantee the uniqueness of strong solutions. The proof proceeds via a time-discrete Rothe approximation and careful elliptic regularity estimates depending in a quantitative way on the (local) convexity of the potential featuring in the model. In the second part of the paper, we show that our strong solutions may be approximated by a fully discrete numerical scheme based on a spatial finite element discretization, whose rate of convergence is consistent with the regularity of strong solutions whose existence and uniqueness are established.

Název v anglickém jazyce

Regularity and approximation of strong solutions to rate-independent systems

Popis výsledku anglicky

Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this work, we prove the existence of Holder-regular strong solutions for a class of rate-independent systems. We also establish additional higher regularity results that guarantee the uniqueness of strong solutions. The proof proceeds via a time-discrete Rothe approximation and careful elliptic regularity estimates depending in a quantitative way on the (local) convexity of the potential featuring in the model. In the second part of the paper, we show that our strong solutions may be approximated by a fully discrete numerical scheme based on a spatial finite element discretization, whose rate of convergence is consistent with the regularity of strong solutions whose existence and uniqueness are established.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

e-ISSN

—

Svazek periodika

27

Číslo periodika v rámci svazku

13

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

46

Strana od-do

2511-2556

Kód UT WoS článku

000413371300005

EID výsledku v databázi Scopus

2-s2.0-85030840996