General results for lumped mass approximation of isoparametric eigenvalue problem on triangular meshes

This paper deals with a FE-numerical quadrature method giving a diagonalization of the mass matrix (lumped mass matrix). The method is applied for a class of second order selfadjoint elliptic operators defined on a bounded domain in the plane. The isoparametric finite element transformations and triangular Lagrange finite elements are used.
The paper concludes with the investigation started by the authors in [2,3] for the isoparametric variant of the lumped mass modification for second order planar eigenvalue problems. Thus the relationship between the possible quadrature formulas and the precision of the method is proved. The effect of these numerical integrations on the error in eigenvalues and eigenfunctions is estimated. At the end of the paper, the numerical results confirming the theory are presented.