Mass-Lumping or not Mass-Lumping for eigenvalue problems

MARÍA G. ARMENTANO, RICARDO G. DURÁN

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

John Wiley & Sons

Año: 2003 vol. 19 p. 653 - 664

0749-159X

eigenvalue problemsIn this paper we analyze the effect of mass-lumping in the linear triangular  finite element approximation  of second order elliptic eigenvalue problems. We prove thatthe 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  theexact eigenvalue when  the mesh size is small enough. So, we concludethat the use of mass-lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggestthat the eigenvalue computed with mass-lumping is below the exact oneif the mesh  is not too coarse.