Superconvergence of discontinuous galerkin solutions for delay differential equations of pantograph type

Qiumei Huang*, Hehu Xie, Hermann BRUNNER

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

This paper is concerned with the superconvergence of the discontinuous Galerkin solutions for delay differential equations with proportional delays vanishing at t = 0. Two types of superconvergence are analyzed here. The first is based on interpolation postprocessing to improve the global convergence order by finding the superconvergence points of discontinuous Galerkin solutions. The second type follows from the integral iteration which just requires a local integration procedure applied to the discontinuous Galerkin solution, thus increasing the order of convergence. The theoretical results are illustrated by a broad range of numerical examples.

Original languageEnglish
Pages (from-to)2664-2684
Number of pages21
JournalSIAM Journal of Scientific Computing
Volume33
Issue number5
DOIs
Publication statusPublished - 2011

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Discontinuous Galerkin method
  • Interpolation and iteration postprocessing
  • Pantograph delay differential equation
  • Superconvergence
  • Vanishing proportional delay

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