Convergence Analysis of Newton–Schur Method for Symmetric Elliptic Eigenvalue Problem

In this paper, we consider the Newton–Schur method in Hilbert space and obtain quadratic convergence. For symmetric elliptic eigenvalue problem discretized by standard finite element nonoverlapping domain decomposition method, use Steklov–Poincaré operator to reduce on into nonlinear subproblem , which is union of subdomain boundaries. We prove that convergence rate for where constant independent fine mesh size coarse are errors after before one iteration step, respectively. specific inner product a sharper obtained, can . Numerical experiments confirm our theoretical analysis.