Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas

AbstractIn this paper we establish the convergence and the rate of convergence for approximate eigenvalues and eigenfunctions of second-order elliptic eigenvalue problems, obtained by a lumped mass finite-element approximation. Various aspects of lumped mass techniques have been discussed for such eigenvalue problems by Fix (1972), Ishihara (1977), Strang and Fix (1973) and Tong et al. (1971), among others. In our approach the lumping of the mass matrix results from the use of a Lobatto quadrature formula for the integrals over rectangular Lagrange finite elements of degree k