Runge–Kutta Time Discretization of Nonlinear Parabolic Equations Studied via Discrete Maximal Parabolic Regularity

Peer C. Kunstmann, Buyang Li, Christian Lubich

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

Abstract

Error bounds are obtained in the (Formula presented.) norm uniformly on bounded time intervals and, with an improved approximation order, in the parabolic energy norm. The proofs rely on discrete maximal parabolic regularity. This is used to obtain (Formula presented.) estimates, which are the key to the numerical analysis of these problems.
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalFoundations of Computational Mathematics
DOIs
Publication statusAccepted/In press - 10 Aug 2017

Keywords

  • Error bounds
  • Gradient flow
  • Maximal parabolic regularity
  • Nonlinear parabolic equation
  • Runge–Kutta method
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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