A variational principle for adaptive approximation of ordinary differential equations

Kyoung Sook Moon*, Anders Szepessy, Raul Tempone, Georgios E. Zouraris

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error = Σ local error · weight, for general approximation of functions of solutions to ordinary differential equations. This error representation is then approximated by a sum of computable error indicators, to obtain a useful global error indicator for adaptive mesh refinements. A uniqueness formulation is provided for desirable error representations of adaptive algorithms.

Original languageEnglish (US)
Pages (from-to)131-152
Number of pages22
JournalNumerische Mathematik
Volume96
Issue number1
DOIs
StatePublished - Jan 1 2003

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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