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 L2 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 L2 error.