Solution of atomic Hartree–Fock equations with the P version of the finite element method

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Abstract
The Hartree–Fock equations for atoms are solved with the p version of the finite element method, which differs from the traditional finite element method in using high order, hierarchic polynomials as basis functions. Recursion formulas are developed for the analytical evaluation of integrals, which are crucial in reducing the computation time and maintaining the accuracy of the solution. A hierarchic computational approach is used where the solution at a certain level is used to start the calculation at the next level. Results are presented for closed and open shell atoms taken from various columns of the periodic table that show excellent agreement with accurate numerical calculations.