<i>A posteriori</i> error estimator for adaptive local basis functions to solve Kohn–Sham density functional theory

• DOI: 10.4310/cms.2015.v13.n7.a5
• Publication Date: 2015-08-19T20:26:58Z
• Authors: Jason Kaye; Lin Lin; Chao Yang
• Keywords: Basis function; Kohn–Sham equations; Basis (linear algebra)

Kohn-Sham density functional theory is one of the most widely used electronic structure theories. The recently developed adaptive local basis functions form an accurate and systematically improvable set for solving using discontinuous Galerkin methods, requiring a small number per atom. In this paper we develop residual-based posteriori error estimates approach, which can be to guide non-uniform refinement highly inhomogeneous systems such as surfaces large molecules. are non-polynomial functions, standard $hp$-refinement polynomial do not directly apply. We generalize functions. demonstrate practical use estimator in performing three-dimensional calculations quasi-2D aluminum single-layer graphene oxide system water.