Homogeneous and heterogeneous domain decomposition methods for plate bending problems

We consider the approximation of fourth-order problems derived, e.g., by the Kirchoff plate model and the heterogeneous coupling between a fourth-order problem and a reduced second-order one, describing, e.g., a plate-membrane model. This paper is devoted to the analysis of an iteration by subdomain method, the so-called Dirichlet/Neumann method, which is used to solve both homogeneous and heterogeneous couplings. Numerical results obtained by the spectral element method are shown.