Continuous galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type

Qiumei Huang, Xiuxiu Xu, Hermann BRUNNER*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We analyze the optimal global and local convergence properties of continuous Galerkin (CG) solutions on quasi-geometric meshes for delay differential equations with proportional delay. It is shown that with this type of meshes the attainable order of nodal superconvergence of CG solutions is higher than of the one for uniform meshes. The theoretical results are illustrated by a broad range of numerical examples.

Original languageEnglish
Pages (from-to)5423-5443
Number of pages21
JournalDiscrete and Continuous Dynamical Systems
Volume36
Issue number10
DOIs
Publication statusPublished - Oct 2016

Scopus Subject Areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

User-Defined Keywords

  • Continuous Galerkin method
  • Nonlinear vanishing delay
  • Pantograph delay differential equation
  • Quasi-geometric mesh
  • Superconvergence

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