On the Postprocessing Technique for Eigenvalue Problems

Abstract

We present a new strategy of accelerating the convergence rate for the finite element solutions of the large class of linear eigenvalue problems of order 2m. The proposed algorithms have the superconvergence properties of the eigenvalues, as well as of the eigenfunctions. This improvement is obtained at a small computational cost. Solving a more simple additional problem, we get good finite element approximations on the coarse mesh. Different ways for calculating the postprocessed eigenfunctions are considered. The case where the spectral parameter appears linearly in the boundary conditions is discussed. The numerical examples, presented here, confirm the theoretical results and show the efficiency of the postprocessing method.