  In this paper, we first study the behavior of inverse mean curvature flow in
Schwarzschild manifold. We show that if the initial hypersurface $\Sigma$ is
strictly mean convex and star-shaped, then the flow hypersurface $\Sigma_t$
converges to a large coordinate sphere as $t\rightarrow \infty$ exponentially.
We also describe an application of this convergence result. In the second part
of this paper, we will analyse the inverse mean curvature flow in
Kottler-Schwarzchild manifold. By deriving a lower bound for the mean curvature
on the flow hypersurface independently of the initial mean curvature, we can
use an approximation argument to show the global existence and regularity of
the smooth inverse mean curvature flow for star-shaped and weakly mean convex
initial hypersurface, which generalizes Huisken-Ilmanen's result [18].
