THE SHIFTED-INVERSE POWER WEAK GALERKIN METHOD FOR EIGENVALUE PROBLEMS

This paper proposes and analyzes a new weak Galerkin method for the eigenvalueproblem by using the shifted-inverse power technique. A high order lower bound canbe obtained at a relatively low cost via the proposed method. The error estimates forboth eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown aswell under some conditions. Numerical examples are presented to validate the theoreticalanalysis.