New substructuring domain decomposition methods for advection-diffusion equations

In this paper we consider a nonsymmetric elliptic problem and we use the techniques related to the Steklov–Poincaré operators to propose new substructuring iterative procedures. In particular, we propose two methods that generalize the well-known Neumann–Neumann and Dirichlet–Neumann iterative procedures. We prove that our methods, that use symmetric and positive-definite preconditioners, lead to the construction of iterative schemes with optimal convergence properties. Numerical results for the finite element discretization are given.