The parabolic $p$-Laplacian with fractional differentiability
Breit D, Diening L, Storn J, Wichmann J (2021)
IMA Journal of Numerical Analysis 41(3): 2110-2138.
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| Veröffentlicht | Englisch
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**Abstract**
We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space–time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskiǐ spaces and therefore cover situations when the (gradient of the) solution has only fractional derivatives in space and time. The main novelty is that, different to all previous results, we do not assume any coupling condition between the space and time resolutions $h$ and $\tau $. For this we show that the $L^2$-projection is compatible with the quasi-norm. The theoretical error analysis is complemented by numerical experiments.
We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space–time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskiǐ spaces and therefore cover situations when the (gradient of the) solution has only fractional derivatives in space and time. The main novelty is that, different to all previous results, we do not assume any coupling condition between the space and time resolutions $h$ and $\tau $. For this we show that the $L^2$-projection is compatible with the quasi-norm. The theoretical error analysis is complemented by numerical experiments.
Erscheinungsjahr
2021
Zeitschriftentitel
IMA Journal of Numerical Analysis
Band
41
Ausgabe
3
Seite(n)
2110-2138
ISSN
0272-4979
eISSN
1464-3642
Page URI
https://pub.uni-bielefeld.de/record/2958034
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Breit D, Diening L, Storn J, Wichmann J. The parabolic $p$-Laplacian with fractional differentiability. IMA Journal of Numerical Analysis. 2021;41(3):2110-2138.
Breit, D., Diening, L., Storn, J., & Wichmann, J. (2021). The parabolic $p$-Laplacian with fractional differentiability. IMA Journal of Numerical Analysis, 41(3), 2110-2138. https://doi.org/10.1093/imanum/draa081
Breit, Dominic, Diening, Lars, Storn, Johannes, and Wichmann, Jörn. 2021. “The parabolic $p$-Laplacian with fractional differentiability”. IMA Journal of Numerical Analysis 41 (3): 2110-2138.
Breit, D., Diening, L., Storn, J., and Wichmann, J. (2021). The parabolic $p$-Laplacian with fractional differentiability. IMA Journal of Numerical Analysis 41, 2110-2138.
Breit, D., et al., 2021. The parabolic $p$-Laplacian with fractional differentiability. IMA Journal of Numerical Analysis, 41(3), p 2110-2138.
D. Breit, et al., “The parabolic $p$-Laplacian with fractional differentiability”, IMA Journal of Numerical Analysis, vol. 41, 2021, pp. 2110-2138.
Breit, D., Diening, L., Storn, J., Wichmann, J.: The parabolic $p$-Laplacian with fractional differentiability. IMA Journal of Numerical Analysis. 41, 2110-2138 (2021).
Breit, Dominic, Diening, Lars, Storn, Johannes, and Wichmann, Jörn. “The parabolic $p$-Laplacian with fractional differentiability”. IMA Journal of Numerical Analysis 41.3 (2021): 2110-2138.
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