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

✍ Scribed by Yan Xu; Chi-Wang Shu

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 364 KB
Volume: 196
Category: Article
ISSN: 0045-7825
DOI: 10.1016/j.cma.2006.10.043

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✦ Synopsis

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.

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