  A new numerical approach is proposed for the simulation of coupled
three-dimensional and one-dimensional elliptic equations (3D-1D coupling)
arising from dimensionality reduction of 3D-3D problems with thin inclusions.
The method is based on a well posed mathematical formulation and results in a
numerical scheme with high robustness and flexibility in handling geometrical
complexities. This is achieved by means of a three-field approach to split the
1D problems from the bulk 3D problem, and then resorting to the minimization of
a properly designed functional to impose matching conditions at the interfaces.
Thanks to the structure of the functional, the method allows the use of
independent meshes for the various subdomains.
