Maximum-norm stability and maximal L<sup>p</sup> regularity of FEMs for parabolic equations with Lipschitz continuous coefficients

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Abstract

In this paper, we study the semi-discrete Galerkin finite element method for parabolic equations with Lipschitz continuous coefficients. We prove the maximum-norm stability of the semigroup generated by the corresponding elliptic finite element operator, and prove the space-time stability of the parabolic projection onto the finite element space in L<sup>∞</sup>(QT) and L<sup>p</sup>((0,T); L<sup>p</sup>(Ω)), 1 < p, q < ∞. The maximal L<sup>p</sup> regularity of the parabolic finite element equation is also established.
Original languageEnglish
Pages (from-to)489-516
Number of pages28
JournalNumerische Mathematik
Volume131
Issue number3
DOIs
Publication statusPublished - 13 Nov 2015
Externally publishedYes

Keywords

  • 35K20
  • 65M12
  • 65M30

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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