Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

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

Language

English

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. © 2011 Society for Industrial and Applied Mathematics.

Keywords

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

Publication Date

2011

Source Publication Title

SIAM Journal on Scientific Computing

Volume

33

Issue

5

Start Page

2664

End Page

2684

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/110824632

Link to Publisher's Edition

http://dx.doi.org/10.1137/110824632

ISSN (print)

10648275

ISSN (electronic)

10957197

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