Discontinuous Galerkin Methods for Convection-Diffusion Equations for Varying and Vanishing Diffusivity
Year: 2009
Author: J. Proft, B. Rivière
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 533–561
Abstract
This work formulates and analyzes a new family of discontinuous Galerkin methods for the time-dependent convection-diffusion equation with highly varying diffusion coefficients, that do not require the use of slope limiting techniques. The proposed methods are based on the standard NIPG/SIPG techniques, but use special diffusive numerical fluxes at some important interfaces. The resulting numerical solutions have an $L^2$ error that is significantly smaller than the error obtained with standard discontinuous Galerkin methods. Theoretical convergence results are also obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-IJNAM-783
International Journal of Numerical Analysis and Modeling, Vol. 6 (2009), Iss. 4 : pp. 533–561
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Numerical fluxes discontinuous Galerkin methods high and low diffusivity $L^2$ error.