hp-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems

Irene Kyza*, Stephen Metcalfe, Thomas P. Wihler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existence in the context of blow-up. The structure of the derived estimator leads naturally to the development of both h and hp versions of an adaptive algorithm designed to approximate the blow-up time. The adaptive algorithms are then applied in a series of numerical experiments, and the rate of convergence to the blow-up time is investigated.

Original languageEnglish
Pages (from-to)111-127
Number of pages17
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - 1 Apr 2018


  • Blow-up singularities
  • Galerkin time stepping schemes
  • High-order methods
  • Initial value problems in Hilbert spaces


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