A finite-element time-domain beam propagation method is described for the solution of electron waveguide discontinuities. Scattering properties in steady state are evaluated with Fourier transform of a pulsed wave in time domain. A perfectly-matched-layer boundary condition is implemented into the electron waveguide simulations. The approach is applied to an electron resonant cavity, and it is confirmed that when treating a slowly varying electron wave function, the converged solution can be obtained with moderate time step size.