  The paper is concerned with the derivation and analysis of nonoverlapping
domain decomposition for heterogeneous, anisotropic diffusion problems
discretized by the finite element cell-centered (FECC) scheme. Differently from
the standard finite element method (FEM), the FECC method involves only cell
unknowns and satisfies local conservation of fluxes by using a technique of
dual mesh and multipoint flux approximations to construct the discrete gradient
operator. Consequently, if the domain is decomposed into nonoverlapping
subdomains, the transmission conditions (on the interfaces between subdomains)
associated with the FECC scheme are different from those of the standard FEM.
However, the substructuring procedure as well as the Neumann-Neumann type
preconditioner can be adapted to the domain decomposition-based FECC method
naturally. Convergence analysis of a preconditioned iterative algorithm, namely
the Dirichlet-Neumann to Neumann-Neumann algorithm, associated with the
discrete FECC interface problem is the main focus of this work. Two dimensional
numerical results for two subdomains with conforming meshes demonstrate that
the preconditioned iterative algorithm converges independently of the mesh size
and the coefficient jump.
