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 - <p style="text-align: justify;">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.</p>