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

Khripunova Balci A, Ortner C, Storn J (2022)
Numerische Mathematik .

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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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
ISSN
0029-599X
eISSN
0945-3245
Page URI
https://pub.uni-bielefeld.de/record/2964346

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Khripunova Balci A, Ortner C, Storn J. Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik . 2022.
Khripunova Balci, A., Ortner, C., & Storn, J. (2022). Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik . https://doi.org/10.1007/s00211-022-01303-1
Khripunova Balci, A., Ortner, C., and Storn, J. (2022). Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik .
Khripunova Balci, A., Ortner, C., & Storn, J., 2022. Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik .
A. Khripunova Balci, C. Ortner, and J. Storn, “Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap”, Numerische Mathematik , 2022.
Khripunova Balci, A., Ortner, C., Storn, J.: Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap. Numerische Mathematik . (2022).
Khripunova Balci, Anna, Ortner, Christoph, and Storn, Johannes. “Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap”. Numerische Mathematik (2022).

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arXiv: 2106.06837

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