Thanks @Carlo Beenakker. I could derive a similar expression that I think it is equivalent to yours. I am editing the question.

Certainly the divergence decreases by one the order of the tensor over which operates. I need the divergence since I'm using the finite volume method to solve them; therefore, the divergence is transformed into a sum by use of the Gauss theorem.

Thanks for your reply @Qfwfq ! Unfortunately I do not know very much about differential forms. Sorry...

Yes @Qfwfq, this something should be a second order tensor field. I have edited the question to be clearer.