Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations

Y. Xu; Chi-Wang Shu

doi:10.1016/j.cma.2006.10.043

Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations

Y. Xu, Chi-Wang Shu

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

In this paper, we provide $L^2$ error estimates for the semi-discrete local discontinuous Galerkin methods for nonlinear convection-diffusion equations and KdV equations with smooth solutions. The main technical difficulty is the control of the inter-element jump terms which arise because of the nonlinearity of the PDEs and the discontinuous nature of the numerical method.

Original language	Undefined
Article number	10.1016/j.cma.2006.10.043
Pages (from-to)	3805-3822
Number of pages	18
Journal	Computer methods in applied mechanics and engineering
Volume	196
Issue number	2/37-40
DOIs	https://doi.org/10.1016/j.cma.2006.10.043
Publication status	Published - 1 Aug 2007

Keywords

Nonlinear convection–diffusion equation
KdV equation
EWI-9464
MSC-65M15
MSC-65M60
METIS-242056
Error estimate
Local discontinuous Galerkin method
IR-63963

Access to Document

10.1016/j.cma.2006.10.043

http://eprints.eemcs.utwente.nl/secure2/9464/01/xu_shu_CMAME_2007.pdf

Cite this

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title = "Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations",

abstract = "In this paper, we provide $L^2$ error estimates for the semi-discrete local discontinuous Galerkin methods for nonlinear convection-diffusion equations and KdV equations with smooth solutions. The main technical difficulty is the control of the inter-element jump terms which arise because of the nonlinearity of the PDEs and the discontinuous nature of the numerical method.",

keywords = "Nonlinear convection–diffusion equation, KdV equation, EWI-9464, MSC-65M15, MSC-65M60, METIS-242056, Error estimate, Local discontinuous Galerkin method, IR-63963",

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T1 - Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations

AU - Xu, Y.

AU - Shu, Chi-Wang

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PY - 2007/8/1

Y1 - 2007/8/1

N2 - In this paper, we provide $L^2$ error estimates for the semi-discrete local discontinuous Galerkin methods for nonlinear convection-diffusion equations and KdV equations with smooth solutions. The main technical difficulty is the control of the inter-element jump terms which arise because of the nonlinearity of the PDEs and the discontinuous nature of the numerical method.

AB - In this paper, we provide $L^2$ error estimates for the semi-discrete local discontinuous Galerkin methods for nonlinear convection-diffusion equations and KdV equations with smooth solutions. The main technical difficulty is the control of the inter-element jump terms which arise because of the nonlinearity of the PDEs and the discontinuous nature of the numerical method.

KW - Nonlinear convection–diffusion equation

KW - KdV equation

KW - EWI-9464

KW - MSC-65M15

KW - MSC-65M60

KW - METIS-242056

KW - Error estimate

KW - Local discontinuous Galerkin method

KW - IR-63963

U2 - 10.1016/j.cma.2006.10.043

DO - 10.1016/j.cma.2006.10.043

M3 - Article

SN - 0045-7825

VL - 196

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EP - 3822

JO - Computer methods in applied mechanics and engineering

JF - Computer methods in applied mechanics and engineering

IS - 2/37-40

M1 - 10.1016/j.cma.2006.10.043

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