Hybridization and Postprocessing Techniques for Mixed Eigenfunctions

Abstract

We introduce hybridization and postprocessing techniques for the Raviart?Thomas approximation of second-order elliptic eigenvalue problems. Hybridization reduces the Raviart?Thomas approximation to a condensed eigenproblem. The condensed eigenproblem is nonlinear, but smaller than the original mixed approximation. We derive multiple iterative algorithms for solving the condensed eigenproblem and examine their interrelationships and convergence rates. An element-by-element postprocessing technique to improve accuracy of computed eigenfunctions is also presented. We prove that a projection of the error in the eigenspace approximation by the mixed method (of any order) superconverges and that the postprocessed eigenfunction approximations converge faster for smooth eigenfunctions. Numerical experiments using a square and an L-shaped domain illustrate the theoretical results.