A domain decomposition method for domains with holes using a complementary decomposition

In this paper, a new non-conforming domain decomposition method based on fictitious domains is considered for linear elasticity problems on domains with holes. Existence and uniqueness of the solution of this alternative approach are showed in the continuous and discrete case. Although the established a priori estimate for the discretization error is not optimal, the scheme is of interest in case of moving geometries and in shape optimization. To solve the arising coupled linear system, we use a block SOR method. The convergence rate does not depend on the mesh size. Numerical results illustrate the flexibility of the discretization scheme.