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 t he interfaces (Steklov-Poincare equations). Via sharp stability estima tes, we prove the convergence of an iterative procedure that gives the solution of the Steklov-Poincare equation for the two-domain case. Wh at precedes is done both for the continuous problem and for its discre tization based on a streamline diffusion finite element method.