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Chemical accuracy serves as an important metric for assessing theeffectiveness of the numerical method in Kohn--Sham density functional theory.It is found that to achieve chemical accuracy, not only the Kohn--Shamwavefunctions but also the Hartree potential, should be approximatedaccurately. Under the adaptive finite element framework, this can beimplemented by constructing the \emph{a posteriori} error indicator based onapproximations of the aforementioned two quantities. However, this way resultsin a large amount of computational cost. To reduce the computational cost, wepropose a novel multi-mesh adaptive method, in which the Kohn--Sham equationand the Poisson equation are solved in two different meshes on the samecomputational domain, respectively. With the proposed method, chemical accuracycan be achieved with less computational consumption compared with the adaptivemethod on a single mesh, as demonstrated in a number of numerical experiments.

Towards chemical accuracy using a multi-mesh adaptive finite element method in all-electron density functional theory