Department of Mathematics
Supercovergence of discontinuous galerkin solutions for delay differential equations of pantograph type
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.
Discontinuous Galerkin method, Interpolation and iteration postprocessing, Pantograph delay differential equation, Superconvergence, Vanishing proportional delay
Source Publication Title
SIAM Journal on Scientific Computing
Society for Industrial and Applied Mathematics
Huang, Qiumei, Hehu Xie, and Hermann Brunner. "Supercovergence of discontinuous galerkin solutions for delay differential equations of pantograph type." SIAM Journal on Scientific Computing 33.5 (2011): 2664-2684.