Convergence Analysis of Domain Decomposition algorithms with full overlapping for the advection-diffusion problems.

: The aim of this paper is to study the convergence properties of a Time Marching Algorithm solving Advection-Diffusion problems on two domains using incompatible discretizations. The basic algorithm is first presented, and theoretical or numerical results illustrate its convergence properties. This study is based on spectral theory, a priori estimates and a Di-Giorgi-Nash maximum principle . Key-words: non symmetric elliptic operators, domain decomposition, incompatible grids, advection-diffusion, time marching algorithms, overlapping, maximun principle. (R'esum'e : tsvp) Universit'e Paris-Dauphine and INRIA, Domaine de Voluceau- Rocquencourt- B.P. 105- Le Chesnay Cedex (France) email: Patrick.LeTallec@inria.fr Department of Mechanical Engineering, Yale University, New Haven, CT 06520 email: tidriri @icase.edu. This work has been done in 1991 at INRIA and has been supported by the Hermes Research program under grant number RDAN 86.1/3. The author is presently supported by the Na..