Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type

Abstract

This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution $U$ and the interpolation $Π_hu$ of the exact solution $u$. The theoretical results are illustrated by numerical examples.