Pointwise a posteriori error bounds for blow-up in the semilinear heat equation

Irene Kyza, Stephen Metcalfe

Research output: Contribution to journalArticlepeer-review

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Abstract

This work is concerned with the development of an adaptive space-time numerical method, based on a rigorous a posteriori error bound, for the semilinear heat equation with a general local Lipschitz reaction term whose solution may blow-up in finite time. More specifically, conditional a posteriori error bounds are derived in the L∞L∞ norm for the first order (Euler) in time, implicit-explicit (IMEX), conforming finite element method in space discretization of the problem. Numerical experiments applied to both blow-up and non blow-up cases highlight the generality of our approach and complement the theoretical results.
Original languageEnglish
Pages (from-to)2609-2631
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume58
Issue number5
Early online date21 Sep 2020
DOIs
Publication statusPublished - 2020

Keywords

  • Semilinear heat equation
  • IMEX method
  • conditional a posteriori error estimates
  • blow-up singularities

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