Extrapolation and a-posteriori error estimators of Petrov-Galerkin methods for non-linear Volterra integro-differential equations

S. H. Zhang, T. Lin, Yanping Lin, M. Rao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.
Original languageEnglish
Pages (from-to)407-422
Number of pages16
JournalJournal of Computational Mathematics
Volume19
Issue number4
Publication statusPublished - 1 Jul 2001
Externally publishedYes

Keywords

  • A-posteriori error estimators
  • Asymptotic expansions
  • Interpolation post-processing
  • Petrov-Galerkin finite element methods
  • Volterra integro-differential equations

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

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