Uniform Error Estimates of a Finite Element Method
          For The Schwarz Alternating Method for more Than
          Two Subdomains.


               M. Boulbrachene and A. Harbi
         Institut de Mathematiques, Universite de Annaba
                B.P 12 Annaba 23000 Algeria

     AMS Subject Classification: 65N30

     Keywords: Schwarz Alternating Method, Domain Decomposition,
               Finite Element.

     Abstract. A generalization of the Schwarz alternating method
     to an arbitrary number od subdomains has been studied in [1].
     In this context, we consider the numerical analysis of the
     second order elliptic problem. The domain decomposition is
     chosen such that every subdomain supports an independent mesh
     and leads to a family of subproblems coupled by a like wave
     relaxation method. These subproblems are properly approximated
     by a piecewise linear finite element method.
     For each subproblem, we get the usual uniform finite element error
     estimate, generalizing the work of [2]. We also give numerical
     experiments to illustrate the theoretical results.


     References

     [1] L. Badea, A Generalization of The Schwarz Alternating Method
     to an Arbitrary Number of subdomains.
     Numer.Math. 55, pp 61-81 (1989)

     [2] M. Boulbrachene, P. Cortey-Dumont and J.C Miellou,
     Mixing Finite Elements and Finite Differences in a Subdomain
     Method. Proc. Int. Symp. On Domain Decomposition Method for
     Partial Differential Equations. pp 198-216.
     SIAM Philadelphia (1988)