This paper deals with some aspects of formulation and implementation of a broadband algorithm with build-in analysis of some dispersive media. The construction of the finite element method (FEM) based on direct integration of Maxwell’s equations and solution of some additional convolution integrals is presented. The broadband, fractional model of permittivity is approximated by a set of some relaxation sub-models. The properties of the 3D time-dependent formulation of the FEM algorithm are determined using a benchmark problem with the Cole-Cole and the Davidson-Cole models. Several issues associated with the implementation and some constraints of the broadband finite element algorithm are presented.