Experiments observe an enhanced superconducting gap over impurities as compared to the clean-bulk value. In order to shed more light on this phenomenon, we perform simulations within the framework of Bogoliubov–de Gennes theory applied to the attractive Hubbard model. The simulations qualitatively reproduce the experimentally observed enhancement effect; it can be traced back to an increased local density of states at the Fermi energy in the metal close to the impurity site. In addition, the simulations display significant differences between a thin [two-dimensional (2D)] and a very thick [three-dimensional (3D)] film. In 2D pronounced Friedel oscillations can be observed, which decay much faster in 3D and therefore are more difficult to resolve. Also, this feature is in qualitative agreement with the experiment.