Mortar coupling for heterogeneous partial differential equations

We are interested in the approximation of 2D elliptic equations with dominated
advection and featuring boundary layers. In order to reduce the computational
complexity, the domain is split into two subregions, the first one
far from the layer, where we can neglect the viscosity effects, and the second
one next to the layer. In the latter domain the original elliptic equation is
solved, while in the former one, the pure convection equation obtained by the
original one by dropping the diffusive term is approximated. The interface
coupling is enforced by the non-conforming mortar method. We consider two
different sets of interface conditions and we compare them for what concerns
both computational efficiency and stability. One of the two sets of interface
conditions turns out to be very effective, especially for very small viscosity
when the mortar formulation of the original elliptic problem on the global
domain can fail.