How should I compute the amount of energy of an EM wave absorbed by a material? Can I just use the divergence of the Poynting vector?
There is another possible approach. You can calculate the flux of the Poynting vector over the boundary of the absorbing volume (http://ocw.mit.edu/resources/res-6-001-electromagnetic-fields-and-energy-spring-2008/chapter-11/11.pdf , 11.1, eq. (1)). I used this approach to calculate the power absorbed in a thin cylinder heated by a broad electromagnetic beam (http://arxiv.org/abs/physics/0405091 , http://arxiv.org/abs/physics/0611169 ). The results were later confirmed in experiments (http://arxiv.org/abs/1109.1626 , http://arxiv.org/abs/1208.0066)