Phase diagrams of elements as a function of pressure and temperature exhibit a variety of physical phenomena of interest. However, there remain multiple systems for which the values of the phase transition pressure and temperature are not accurately known. Experimental studies of phase equilibria can be uncertain because of the difficulty to control the stress conditions, kinetics of phase transitions and other experimental constraints. Ab-initio studies are an alternative route to study the phase diagrams of elements by calculating the free energy of the phases under consideration. The Helmholtz free energy is assumed to consist of three contributions: (i) the cold energy curve, (ii) the electronic excitations (in metals) and (iii) the vibrational free energy. The objective of the present study is to explore the accuracy of the ab-initio phase diagram predictions. For this purpose, the following phase transitions were considered: alpha-omega in Ti and Zr (metal-metal), omega-beta in Zr (metal-metal) and diamond-beta tin in silicon (insulator-metal). For all these cases an analysis of the band structure and phonon spectrum was performed to have better insight into these transitions. We found in several case studies that the major differences in the calculated phase diagrams between the different exchange-correlation functionals manifested themselves in the cold curves while the vibrational contributions to the free energy remain similar. For example, in Ti it is found that the phase transition pressure calculated using the general gradient approximation predicts a negative alpha-omega phase transition pressure up to 600 Kelvin while this pressure is positive in the experiment.