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.