Two grid discretization scheme for nonlinear eigenvalues problems

Many mathematical models in science and engineering give rise to nonlinear eigenvalue problems. Let us mention for instance the Gross-Pitaevskii equation describing the steady-states of Bose-Einstein condensates, or the Hartree-Fock and Kohn-Sham equations used to calculate ground state (electronic structures of molecular systems in quantum chemistry and materials science.

Since solving these problems is quite expensive, we propose new methods to simplify this computation. To understand the effect of this simplification on the accuracy of the result, we need some a priori errors estimates of the discretization for variational approximations of the ground state energy, eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems. These results were used for the implementation and the numerical analysis of
two-grid discretization schemes for nonlinear eigenvalue problem.