A flexible tool, based on the finite-element method, for the computational simulation of vortex phenomena in type-II superconductors has been developed. These simulations use refined or newly developed phenomenological models including a time-dependent Ginzburg-Landau model, a variable-thickness thin-film model, simplified models valid for high values of the Ginzburg-Landau parameter, models that account for normal inclusions and Josephson effects, and the Lawrence-Doniach model for layered superconductors. Here, sample results are provided for the case of constant applied magnetic fields. Included in the results are cases of flux pinning by impurities and by thin regions in films.