Numerical analysis of nonlinear eigenvalue problems

International audienceWe provide a priori error estimates for variational approximations of the ground state eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems . We focus in particular on the Fourier spectral approximation (for periodic problems) and on the P1 and P2 finite-element discretizations. Our analysis extends to the case of nonlinear eigenproblems the classical results about the comparative speeds of convergence of the eigenvalues with respect to the eigenvectors in the H1- norm. We show that under some assumptions we recover a standard result for linear elliptic eigenvalue problems