Adaptive Finite Element Approximations for Kohn-Sham Models

Understand

The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences.

• In this paper, we study the adaptive finite element approximations for the Kohn-Sham model.
• Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations.
• Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity.