Titre : Edge-based stabilization and the discrete maximum principle for convection-diffusion equations

In this talk, I will review recent results on the analysis and
numerical performance of different stabilized methods based on the
addition of nonlinear edge-based diffusion to the discrete
formulation. One particular method arising from this approach is the
Algebraic Flux Correction scheme, and then, in particular, an analysis
of this method is given. Several positive (and negative) results are
proven, and a unified analysis of the different methods is presented.
The role of linearity preservation is also discussed, showing that
this property has a positive effect on the performance of the method.
The sharpness of these results is stated via numerical experiments.
Finally, an a posteriori error bound for this approach is presented
and analyzed.