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.