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Regularity and approximation of strong solutions to rate-independent systems
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Rindler, Filip, Schwarzacher, Sebastian and Süli, Endre (2017) Regularity and approximation of strong solutions to rate-independent systems. Mathematical Models & Methods in Applied Sciences, 27 (13). 2511 . doi:10.1142/S0218202517500518 ISSN 0218-2025.
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Official URL: https://doi.org/10.1142/S0218202517500518
Abstract
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 Hölder-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.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Differential equations, Partial, Differential equations, Banach spaces, Finite element method | ||||||||
| Journal or Publication Title: | Mathematical Models & Methods in Applied Sciences | ||||||||
| Publisher: | World Scientific Publishing | ||||||||
| ISSN: | 0218-2025 | ||||||||
| Official Date: | 15 December 2017 | ||||||||
| Dates: |
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| Volume: | 27 | ||||||||
| Number: | 13 | ||||||||
| Article Number: | 2511 | ||||||||
| DOI: | 10.1142/S0218202517500518 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 17 August 2017 | ||||||||
| Date of first compliant Open Access: | 5 October 2018 | ||||||||
| RIOXX Funder/Project Grant: |
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