Projection and iterated projection methods for nonliear integral equations
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Numerical investigation of the pantograph equation
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
SIAM Journal on Numerical Analysis
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
Mathematics of Computation
A Posteriori Error Estimates Based on the Polynomial Preserving Recovery
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
A New Finite Element Gradient Recovery Method: Superconvergence Property
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Postprocessing for the Discontinuous Galerkin Method over Nonuniform Meshes
SIAM Journal on Scientific Computing
Local derivative post-processing for the discontinuous Galerkin method
Journal of Computational Physics
Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type
SIAM Journal on Numerical Analysis
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
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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.