Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap

Khripunova Balci, Anna; Ortner, Christoph; Storn, Johannes

Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap

Khripunova Balci A, Ortner C, Storn J (2022)
Numerische Mathematik 151: 779–805 .

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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DOI

https://doi.org/10.1007/s00211-022-01303-1

URN

urn:nbn:de:0070-pub-29643463

Autor*in

Khripunova Balci, Anna^UniBi ; Ortner, Christoph; Storn, Johannes^UniBi

Einrichtung

Fakultät für Mathematik

Abstract / Bemerkung

We investigate the convergence of the Crouzeix-Raviart finite element method for variational problems with non-autonomous integrands that exhibit non-standard growth conditions. While conforming schemes fail due to the Lavrentiev gap phenomenon, we prove that the solution of the Crouzeix-Raviart scheme converges to a global minimiser. Numerical experiments illustrate the performance of the scheme and give additional analytical insights.

Stichworte

65M12; 65M60

Erscheinungsjahr

2022

Zeitschriftentitel

Numerische Mathematik

Band

151

Seite(n)

779–805

Urheberrecht / Lizenzen

Creative Commons Namensnennung 4.0 International Public License (CC-BY 4.0)

ISSN

0029-599X

eISSN

0945-3245

Finanzierungs-Informationen

Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.

Page URI

https://pub.uni-bielefeld.de/record/2964346

Zitieren

Khripunova Balci A, Ortner C, Storn J. Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik . 2022;151:779–805 .

Khripunova Balci, A., Ortner, C., & Storn, J. (2022). Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik , 151, 779–805 . https://doi.org/10.1007/s00211-022-01303-1

Khripunova Balci, Anna, Ortner, Christoph, and Storn, Johannes. 2022. “Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap”. Numerische Mathematik 151: 779–805 .

Khripunova Balci, A., Ortner, C., and Storn, J. (2022). Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik 151, 779–805 .

Khripunova Balci, A., Ortner, C., & Storn, J., 2022. Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik , 151, p 779–805 .

A. Khripunova Balci, C. Ortner, and J. Storn, “Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap”, Numerische Mathematik , vol. 151, 2022, pp. 779–805 .

Khripunova Balci, A., Ortner, C., Storn, J.: Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik . 151, 779–805 (2022).

Khripunova Balci, Anna, Ortner, Christoph, and Storn, Johannes. “Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap”. Numerische Mathematik 151 (2022): 779–805 .

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