In this paper, numerical result of simulating various linear and nonlinear photonic devices using the finite element based-vector and scalar beam propagation methods are presented. The application of this newly-developed vector finite element based beam propagation method to problems involving radiation losses, like leaky-mode and bent optical waveguide devices is shown, and a study of a novel arrangement invovling three-coupled cores working as a polarization-insensitive optical filter is demonstrated. Also, scalar BPM algorithms based on finite elements have been developed and applied to nonlinear problems, like second harmonic generation and soliton switching in nonlinear fiber couplers.