Kohn-Sham density functional theory (KSDFT) is one of the most successful approximate models for many body problems. Besides computational quantum chemistry, condensed matter physics, etc., KSDFT has also been playing an important role in the study of the nano-optics. For example, multi-physical models are derived with KSDFT to describe surface-enhanced Raman scattering spectroscopy. Recently, there are also works on using time-dependent KSDFT to explain the interaction between intense laser pulse and electronic structures. These new progress on theory and models drives the development of the numerical method. In this talk, a framework of adaptive finite element solutions of Kohn-Sham and time-dependent Kohn-Sham equations as well as its realization in our C++ library AFEABIC are introduced. We will use high harmonic generation, which is a classical phenomenon in the nonlinear optics, as the example to describe the numerical challenges and our methods in AFEABIC.