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A domain decomposition method for solving a Helmholtz-like problem in elasticity based on the Wilson nonconforming element. (English) Zbl 0877.73061
A parallelizable iterative procedure based on a domain decomposition technique is proposed and analyzed for a sequence of elliptic systems with first-order absorbing boundary conditions. This sequence of systems, which are not coercive and have characteristics similar to the Helmholtz equation, describes the motion of a nearly elastic solid in the frequency domain. As an application, the procedure is used to solve an approximation to elliptic systems by Wilson non-conforming finite elements. The convergence of the procedure is demonstrated, and the rate of convergence is obtained when the domain can be decomposed into subdomains consisting of an individual element associated with the Wilson finite element method. The hybridization of the Wilson elements is essentially used in the construction of the discrete procedure.

74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
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