We present the current status of the finite-element method for large-scale atomistic simulations based on the density-functional theory. After a brief overview of our formulation, we describe recent developments, including the optimal choice of adaptive coordinates, an efficient implementation of the ground-state calculations, and a remedy for the eggbox effect. As a new application of our formulation, we present ab initio molecular dynamics simulations on sulfonated poly(4-phenoxybenzoyl-1,4-phenylene) (SPPBP), which is a typical example of polymer electrolyte membranes for fuel cells.