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Volume 6, Issue 4
Discontinuous Galerkin Methods for Convection-Diffusion Equations for Varying and Vanishing Diffusivity

J. Proft & B. Rivière

Int. J. Numer. Anal. Mod., 6 (2009), pp. 533-561.

Published online: 2009-06

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  • 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.

  • Keywords

Numerical fluxes, discontinuous Galerkin methods, high and low diffusivity, $L^2$ error.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-533, author = {Proft , J. and Rivière , B.}, title = {Discontinuous Galerkin Methods for Convection-Diffusion Equations for Varying and Vanishing Diffusivity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/783.html} }
TY - JOUR T1 - Discontinuous Galerkin Methods for Convection-Diffusion Equations for Varying and Vanishing Diffusivity AU - Proft , J. AU - Rivière , B. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 533 EP - 561 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/783.html KW - Numerical fluxes, discontinuous Galerkin methods, high and low diffusivity, $L^2$ error. AB -

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.

Proft , J. and Rivière , B.. (2009). Discontinuous Galerkin Methods for Convection-Diffusion Equations for Varying and Vanishing Diffusivity. International Journal of Numerical Analysis and Modeling. 6 (4). 533-561. doi:
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