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

Qiumei  Huang; Xiuxiu  Xu; Hermann Brunner

doi:10.3934/dcds.2016039

Article Contents

2016, Volume 36, Issue 10: 5423-5443. Doi: 10.3934/dcds.2016039

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

1.
Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124
2.
Department of Mathematics, Hong Kong Baptist University, Hong Kong

Received: August 31, 2015

Revised: November 30, 2015

Published: May 2017

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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.

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Mathematics Subject Classification: 65L03, 65L60, 65L70.

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