Local analysis of the local discontinuous Galerkin method with generalized alternating numerical flux for one-dimensional singularly perturbed problem
type: Item
instance of: scholarly article
title: Local analysis of the local discontinuous Galerkin method with generalized alternating numerical flux for one-dimensional singularly perturbed problem
zbMATH Open document ID: 1382.65308
author: Yao Cheng
author: Qiang Zhang
published in: Journal of Scientific Computing
publication date: 2017-11-10T00:00:00Z
review text: The authors perform the local analysis of the local discontinuous Galerkin (LDG) method based on the generalized alternating flux to solve the one-dimensional time-dependent singularly perturbed problem. The semi-discrete LDG scheme and a fully discrete scheme with explicit time marching are considered. Based on the elemental stability with a suitable weight function we can establish the local stability and local error estimate. The double-optimal local error estimate is also obtained and it is shown that the projection error has the exponential decay property. Some numerical examples are performed that indicate the existence of the double optimal local estimates implying that the results could also be extended to nonlinear cases. Some lemmas and theorems are stated and proved.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 6805227
zbMATH Keywords: local discontinuous Galerkin method
zbMATH Keywords: generalized alternating numerical flux
zbMATH Keywords: singularly perturbed problem
zbMATH Keywords: semidiscretiaztion
zbMATH Keywords: stability
zbMATH Keywords: error estimate
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: s10915-017-0378-y
OpenAlex ID: W2588568969
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DOI: 10.1007/S10915-017-0378-Y
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description: scientific article; zbMATH DE number 6805227