On a domain decomposition for the transport equation: Theory and finite element approximation

We describe a domain decomposition method applied to a boundary value problem for a transport equation in two dimensions. This decomposition leads to a family of problems coupled through suitable equations on the interfaces (Steklov-Poincaré equations). Via sharp stability estimates, we prove the convergence of an iterative procedure that gives the solution of the Steklov- Poincaré equation for the two-domain case. What precedes is done both for the continuous problem and for its discretization based on a streamline diffusion finite element method.