Magnetic reconnection can be interpreted as a process in which the electromagnetic field is frozen into a four-velocity field in Minkowski space. For reconnection to occur the four-velocity field has to be a special type of stagnation flow. Prescribing this type of flow in a finite spatial domain allows the modelling of localized reconnection events and the investigation of examples of reconnection in regions without magnetic nulls. In the present contribution, we start with a simple twisted magnetic flux tube. Reconnection occuring along a part of the axis of the tube results in a structure of the magnetic field which is a superposition of a two-dimensional X-type magnetic field well-known from stationary 2D reconnection models, and a component resulting from the magnetic field parallel to the axis. For localized reconnection, the latter component of the magnetic field evolves in a non-trivial way. This evolution is important for the spatial variation of the parallel electric field integrated along the magnetic field lines. The integrated electric field gives an upper limit for the energy to which particles can be accelerated in a reconnection event and its distribution shows to be localized in very thin structures.