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

Irene Kyza, Stephen Metcalfe

Research output: Contribution to journalArticlepeer-review


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 LcoLco norm for the first order (Euler) in time, implicit-explicit, 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
Issue number5
Publication statusPublished - 2020


  • Blow-up singularities
  • Conditional a posteriori error estimates
  • IMEX method
  • Semilinear heat equation


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