@Article{IJNAM-6-4, 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/2009-IJNAM-783}, url = {https://global-sci.com/article/83667/discontinuous-galerkin-methods-for-convection-diffusion-equations-for-varying-and-vanishing-diffusivity} }