R.R. Parashkevov T.F. Russell J. D. Wilson X. Ye Z. Cai 2003 We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established. application/pdf 10.1137/S0036142996296935 en Domain decomposition for a mixed finite element method in three dimensions article