Discontinuous Galerkin Methods for Convection-Diffusion Equations for Varying and Vanishing Diffusivity

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.

Author Details

J. Proft

B. Rivière