Mass-lumping or not mass-lumping for eigenvalue problems

In this article we analyze the effect of mass-lumping in the linear triangular finite element approximation of second-order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass-lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass-lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass-lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass-lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003