Approximation of the eigenvalue problem for elliptic operator by finite element method with numerical integration

Abstract

The author considers the effect of numerical integration in the case of solving a two-dimensional eigenvalue problem for the second-order elliptic differential operator via the finite element method. It is proved that the optimal estimates for eigenfunctions (namely, the estimates of the same order as the optimal estimates for the classical finite element approximation without numerical integration) are valid under the assumption that the precision of the numerical quadrature is the same as that for the corresponding boundary value problem.