Superconvergence Postprocessing for Eigenvalues

Abstract The main goal of this paper is to present a new strategy of increasing the convergence rate for the numerical solution of the linear finite element eigenvalue problems. This is done by introducing a postprocessing technique for eigenvalues. The postprocessing technique deals with solving a corresponding linear elliptic problem. We prove that the proposed algorithm has the superconvergence property of the eigenvalues and this improvement is attained at a small computational cost. Thus, good finite element approximations for eigenvalues are obtained on the coarse mesh. The numerical examples presented and discussed here show that the resulting postprocessing method is computationally more efficient than the method to which it is applied.

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