  Often computational models are too expensive to be solved in the entire
domain of simulation, and a cheaper model would suffice away from the main zone
of interest. We present for the concrete example of an evolution problem of
advection reaction diffusion type a heterogeneous domain decomposition
algorithm which allows us to recover a solution that is very close to the
solution of the fully viscous problem, but solves only an inviscid problem in
parts of the domain. Our new algorithm is based on the factorization of the
underlying differential operator, and we therefore call it factorization
algorithm. We give a detailed error analysis, and show that we can obtain
approximations in the viscous region which are much closer to the viscous
solution in the entire domain of simulation than approximations obtained by
other heterogeneous domain decomposition algorithms from the literature.
