  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.
