Transport Phenomena problem coupled by Chemical Reactions: Negative values in Finite-element functions lead to numerical divergence

Hi,

it is a well known phenomenon that standard Finite Element discretizations and Advection-Diffusion equations don’t get along well, where problems including artificial oscillations and numerical damping may arise.
There are many techniques to somewhat obviate these issues. A nice overview is this work. There are also a couple of papers on this topic by G. Wells, one of the lead developers of Dolfin, e.g. this one.