A Mixed Finite Element Domain Decomposition Method for Nearly 
          Elastic Wave Equations in the Frequency Domain

                      Xiaobing Feng
                   Department of Mathematics
                   The University of Tennessee
                   Knoxville, Tn 37996


In this paper, a non--overlapping domain decomposition iterative method is
proposed and analyzed for mixed finite element methods for a sequence of
noncoercive elliptic systems with radiation boundary conditions. These
differential systems describe the motion of a nearly elastic solid in the
frequency domain. The convergence of the iterative procedure is demonstrated
and the rate of convergence is derived for the case when the domain is
decomposed into subdomains in which each subdomain consists of an individual
element associated with the mixed finite elements. The hybridization of mixed
finite element methods plays a important role in the construction of the
discrete procedure.