New a Priori FEM Error Estimates for Eigenvalues

"We analyze the Ritz method for symmetric eigenvalue problems and prove a priori eigenvalue error estimates. For a single eigenvalue, we prove an error estimate that depends mainly on just the approximability of the corresponding eigenfunction and provide explicit values for all constants. For a multiple eigenvalue we prove, in addition, apparently the first truly a priori error estimates that show the levels of the eigenvalue errors depending on approximability of eigenfunctions in the corresponding eigenspace."--Authors' abstract.