A genuinely stable Lagrange-Galerkin scheme for convection-diffusion problems

We present a Lagrange-Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange-Galerkin schemes may encounter the instability caused by numerical quadra...

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Bibliographic Details
Published inarXiv.org
Main Authors Tabata, Masahisa, Uchiumi, Shinya
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.05.2015
Subjects
Convection-diffusion equation
Galerkin method
Stability
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Summary:We present a Lagrange-Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange-Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. We prove the stability and convergence of the best possible order. Numerical results reflect these estimates.
ISSN:2331-8422