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

Irene Kyza (Lead / Corresponding author), Stephen Metcalfe, Thomas P. Wihler

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
189 Downloads (Pure)

Abstract

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 stucture 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
Volume75
Early online date27 Sep 2017
DOIs
Publication statusPublished - Apr 2018

Keywords

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

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