TY - JOUR
T1 - Superconvergence of Discontinuous Galerkin Solutions for Delay Differential Equations of Pantograph Type
AU - Huang, Qiumei
AU - Xie, Hehu
AU - Brunner, Hermann
N1 - Funding information:
t College of Applied Sciences, Beijing University of Technology, Beijing 100124, China (qmhuang@ bjut.edu.cn). This author was supported by the National Natural Science Foundation (11101018) and by Beijing Natural Science Foundation (1112002) of China.
$ LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China ([email protected]). This author’s research was supported by the National Natural Science Foundation of China (11001259).
§ Department of Mathematics & Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada A1C 5S7, and Department of Mathematics, Hong Kong Baptist University, Hong Kong, China ([email protected]). This author’s research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant 9406).
Publisher copyright:
Copyright © 2011 Society for Industrial and Applied Mathematics
PY - 2011/10/25
Y1 - 2011/10/25
N2 - 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.
AB - 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.
KW - Discontinuous Galerkin method
KW - Interpolation and iteration postprocessing
KW - Pantograph delay differential equation
KW - Superconvergence
KW - Vanishing proportional delay
UR - http://www.scopus.com/inward/record.url?scp=81555213061&partnerID=8YFLogxK
U2 - 10.1137/110824632
DO - 10.1137/110824632
M3 - Journal article
AN - SCOPUS:81555213061
SN - 1064-8275
VL - 33
SP - 2664
EP - 2684
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 5
ER -