Supercloseness Between the Elliptic Projection and the Approximate Eigenfunction and Its Application to a Postprocessing of Finite Element Eigenvalue Problems

摘要

An estimate confirming the supercloseness between the Ritz projection and the corresponding eigenvectors, obtained by finite element method, is hereby proved. This result is true for a large class of self-adjoint 2m—order elliptic operators. An application of this theorem to the superconvergence postprocessing patch-recovery technique for finite element eigenvalue problems is also presented. Finally, the theoretical investigations are supported by numerical experiments.