  The magnetic Laplacian on a planar domain under a strong constant magnetic
field has eigenvalues close to the Landau levels. We study the case when the
domain is a disc and the spectrum consists of branches of eigenvalues of one
dimensional operators. Under Neumann boundary condition and strong magnetic
field, we derive asymptotics of the eigenvalues with accurate estimates of
exponentially small remainders. Our approach is purely variational and applies
to the Dirichlet boundary condition as well, which allows us to recover recent
results by Baur and Weidl.
