  In this paper, we derive a posteriori error estimates for mixed-dimensional
elliptic equations exhibiting a hierarchical structure. Exploiting the exterior
calculus perspective of such equations, we introduce mixed-dimensional
variables and operators, which, together with careful construction of the
functional spaces, allow us to recast the set of partial differential equations
as a regular linear elliptic problem structure-wise. We therefrom apply the
well-established theory of functional a posteriori error estimates to our model
to derive guaranteed abstract as well as fully computable upper bounds. Our
estimators are tested using three different families of locally-mass
conservative methods on synthetic problems and verification benchmarks of flow
in fractured porous media. The numerical results support our theoretical
findings while showcasing satisfactory effectivity indices.
