  The theory of intersection spaces assigns cell complexes to certain
stratified topological pseudomanifolds depending on a perversity function in
the sense of intersection homology. The main property of the intersection
spaces is Poincar\'e duality over complementary perversities for the reduced
singular (co)homology groups with rational coefficients. This (co)homology
theory is not isomorphic to intersection homology, instead they are related by
mirror symmetry. Using differential forms, Banagl extended the intersection
space cohomology theory to 2-strata pseudomanifolds with a geometrically flat
link bundle. In this paper we use differential forms on manifolds with corners
to generalize the intersection space cohomology theory to a class of 3-strata
spaces with flatness assumptions for the link bundles. We prove Poincar\'e
duality over complementary perversities for the cohomology groups. To do so, we
investigate fiber bundles on manifolds with boundary. At the end, we give
examples for the application of the theory.
