The parabolic p-Laplacian with fractional differentiability

Dominic Breit, Lars Diening, Johannes Storn, Jörn Wichmann

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4 Citations (Scopus)

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 Nikolskii 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 τ . For this we show that the L2-projection is compatible with the quasi-norm. The theoretical error analysis is complemented by numerical experiments.

Original languageEnglish
Pages (from-to)2110-2138
Number of pages29
JournalIMA Journal of Numerical Analysis
Volume41
Issue number3
DOIs
Publication statusPublished - 1 Jul 2021
Externally publishedYes

Keywords

  • Finite element methods
  • Nonlinear Laplace-type systems
  • P-heat equation
  • Parabolic PDEs
  • Space-time discretization

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