For a circuit, for example, there is a voltage source in a simple circuit, and the voltage source is followed by a resistance. For such a circuit, the energy transfer from the battery to the resistance is the energy flow corresponding to the Poynting vector in space.  

But for two separate circuits, such as the primary coil of a transformer followed by the power supply, and the secondary coil followed by the load resistance, the corresponding energy transfer energy of Poynting vector is not all right. In this case, the energy flow corresponding to Poynting vector must be decomposed into three parts: (1) Poynting energy flow of primary coil electromagnetic field, (2) energy flow of secondary coil electromagnetic field, and (3) energy flow corresponding to mixed term. The energy flow of the primary coil and the energy flow of the secondary coil belong to the self energy flow, and the energy flow of the mixed term is the mutual energy flow. Because the self-energy flow is pure imaginary, it does not transfer energy on average. The mutual energy flow can be a real number, so it can be responsible for transferring energy. for details please see the reference:http://pubs.sciepub.com/ijp/11/1/4/index.html

In the following figure, the mutual energy flow have been used to calculate the energy flow from primary coil to the secondary coil. The self-energy flow (corresponding to the Poynting vector) failed to do so.
 

For a circuit, for example, there is a voltage source in a simple circuit like above, and the voltage source is followed by a resistance. For such a circuit, the energy transfer from the battery to the resistance is the energy flow corresponding to the Poynting vector in space. 

But for two separate circuits, such as the primary coil of a transformer followed by the power supply, and the secondary coil followed by the load resistance, the corresponding energy transfer energy of Poynting vector is not all right. In this case, the energy flow corresponding to Poynting vector must be decomposed into three parts: (1) Poynting energy flow of primary coil electromagnetic field, (2) energy flow of secondary coil electromagnetic field, and (3) energy flow corresponding to mixed term. The energy flow of the primary coil and the energy flow of the secondary coil belong to the self energy flow, and the energy flow of the mixed term is the mutual energy flow. Because the self-energy flow is pure imaginary, it does not transfer energy on average. The mutual energy flow can be a real number, so it can be responsible for transferring energy. for details please see the reference:http://pubs.sciepub.com/ijp/11/1/4/index.html

In the following figure, the mutual energy flow have been used to calculate the energy flow from primary coil to the secondary coil. The self-energy flow (corresponding to the Poynting vector) failed to do so.