Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations

Georgios Akrivis, Buyang Li, Christian Lubich

Research output: Journal article publicationJournal articleAcademic researchpeer-review

32 Citations (Scopus)

Abstract

We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic regularity and energy estimates to derive optimal-order error bounds for the time-discrete approximation to the solution and its gradient in the maximum norm and energy norm.
Original languageEnglish
Pages (from-to)1527-1552
Number of pages26
JournalMathematics of Computation
Volume86
Issue number306
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • BDF methods
  • Energy technique
  • Maximal regularity
  • Maximum norm estimates
  • Parabolic equations
  • Stability

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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