Résumé
The purpose of this PHD thesis is the study of a domain decomposition method: the Mortar method. The Mortar method has the advantage to allow for non-matching grids at the interfaces between subdomains of a non overlapping domain decomposition. The domain is divided into several parts, and independant finite element discretization is used on each subdomain. <br />It is designed to provide an efficient parallelizable evaluation and solution framework. The discretization leads to an algebraic saddle-point problem solved by a conjugate gradient method. Lagrange multipliers are then introduced to enforce continuity constraints between the local finite element approximations. Differents preconditioners are studied: the first one is based on the direct extension of the lumped preconditioner, the other one is based on a hierarchical basis of the space of the Lagrange multipliers. Finally, the third one is a block diagonal preconditioner. Then, an extension of the Mortar method to the D.K.T. method for shells problems is studied both from the numerical analysis (convergence) and computing point of view.