A new nonsymmetric discontinuous Galerkin method for time dependent convection diffusion equations
type: Item
instance of: scholarly article
title: A new nonsymmetric discontinuous Galerkin method for time dependent convection diffusion equations
zbMATH Open document ID: 1269.65102
author: Jue Yan
published in: Journal of Scientific Computing
publication date: 2013-04-08T00:00:00Z
review text: The paper describes a nonsymmetric discontinuous Galerkin method for time dependent convection-diffusion equations. The method is introduced with a one-dimensional setting, establishes criteria for nonlinear stability and presents an estimate for the energy norm. Further, the method is extended for two-dimensional diffusion equations. Several numerical examples -- linear heat diffusion, nonlinear convection-diffusion equation, nonlinear reaction-diffusion equation, nonlinear diffusion in porous media and degenerate parabolic equations -- are considered to establish the utility of the method. In all these cases, the numerical errors are well within the bound. The scheme is well suited for parabolic differential equations.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76M10
zbMATH DE Number: 6151377
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: degenerate parabolic equation
zbMATH Keywords: nonsymmetric discontinuous Galerkin method
zbMATH Keywords: time dependent convection-diffusion equations
zbMATH Keywords: linear heat diffusion
zbMATH Keywords: nonlinear convection-diffusion equation
zbMATH Keywords: nonlinear reaction-diffusion equation
zbMATH Keywords: nonlinear diffusion in porous media
MaRDI profile type: Publication
full work available at URL: s10915-012-9637-0
OpenAlex ID: W2084788717
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DOI: 10.1007/S10915-012-9637-0
description: scientific article; zbMATH DE number 6151377