Real Space Approach to Electronic-Structure Calculations
  We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform mesh is made possible, thus enabling us to deal with localized systems with ease. To illustrate the utility of this method, we perform an all-electron calculation of hydrogen molecule in a supercell with LDA approximation. Our method is also applicable to mesoscopic systems. 
Eiji Tsuchida and Masaru Tsukada