  In this paper, we revisit the nonoverlapping domain decomposition methods for
solving elliptic problems with high contrast coefficients. Some interesting
results are discovered. We find that the Dirichlet-Neumann algorithm and
Robin-Robin algorithms may make full use of the ratio of coefficients.
Actually, in the case of two subdomains, we show that their convergence rates
are $O(\epsilon)$, if $\nu_1\ll\nu_2$, where $\epsilon = \nu_1/\nu_2$ and
$\nu_1,\nu_2$ are coefficients of two subdomains. Moreover, in the case of many
subdomains, the condition number bounds of Dirichlet-Neumann algorithm and
Robin-Robin algorithm are $1+\epsilon(1+\log(H/h))^2$ and
$C+\epsilon(1+\log(H/h))^2$, respectively, where $\epsilon$ may be a very small
number in the high contrast coefficients case. Besides, the convergence
behaviours of the Neumann-Neumann algorithm and Dirichlet-Dirichlet algorithm
may be independent of coefficients while they could not benefit from the
discontinuous coefficients. Numerical experiments are preformed to confirm our
theoretical findings.
