  We present a density functional theory (DFT) based supercell approach for
modeling small polarons with proper account for the long-range elastic response
of the material. Our analysis of the supercell dependence of the polaron
properties (e.g., atomic structure, binding energy, and the polaron level)
reveals long-range electrostatic effects and the electron-phonon interaction as
the two main contributors. We develop a correction scheme for DFT polaron
calculations that significantly reduces the dependence of polaron properties on
the DFT exchange-correlation functional and the size of the supercell in the
limit of strong electron-phonon coupling. Using our correction approach, we
present accurate all-electron full-potential DFT results for small polarons in
rocksalt MgO and rutile TiO$_2$.
