ABSTRACT
The diffusion-advection-reaction boundary value problems often appear in different applications of physics and mechanics, for example, in the processes with diffusion mechanisms, advective transportation and chemical reactions. In addition, it is well known that a large difference between the advective-diffusive transport rate and the rate of chemical reactions results in singular perturbations of these problems. The solutions of such problems and their gradients change so much that the classic schemes of the finite element method (FEM) lose their stability and, as a result, the expected accuracy. We refer to the monographs (Ainsworth & Oden 1997, Braess 2007, Morton 1996, Roos, Stynes, &Tobishka 2008) for an overview and to (Eriksson, Estep, Hansbo, & Johnson 1996, Gratsch & Bathe 2005, Kozarevska & Shynkarenko 2000, Mekchay & Nochetto 2002, Verfurth 1998) for the some recent works on discretization and solution schemes for such problems.
