In [Dai et al, Multi. Model. Simul., 2020], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory, based on which a linearized method was developed in [Hu, et al, EAJAM, accepted] for further improving the numerical efficiency. In this paper, a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham model. Temporally, the convergence, the asymptotic stability, as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works, while spatially, the convergence of the h-adaptive mesh method is demonstrated following [Chen et al, Multi. Model. Simul., 2014], with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham model. Numerical examples confirm the theoretical results very well.

翻译：在[Dai等人, Multi. Model. Simul., 2020]中，针对Kohn-Sham密度泛函理论中的基态计算提出了一种保结构梯度流方法，随后[Hu等人, EAJAM, 已接收]在此基础上发展了一种线性化方法以进一步提高数值效率。本文对该线性化方法在全电子Kohn-Sham模型中的收敛性进行了完整分析。在时间方向上，本文在前人工作基础上讨论了该线性化数值格式的收敛性、渐近稳定性及保结构性质；在空间方向上，本文遵循[Chen等人, Multi. Model. Simul., 2014]的研究，通过关键分析全电子Kohn-Sham模型中Kohn-Sham势的有界性，证明了h自适应网格方法的收敛性。数值算例充分验证了理论结果。