Postprocessing and improved accuracy of the lowest-order mixed finite element approximation for biharmonic eigenvalues

Abstract

The mixed finite element method for the biharmonic eigenvalue problem using linear or bilinear finite elements is considered. The paper is based on approach described by the same authors in [1], where polynomials of degree n, n ≥ 2, were used. The case of linear finite elements was studied by Ishihara in [5], where an error estimate of rate Ο(h1/2) for the eigenvalues and the eigenfunctions was established. Using postprocessing we derive an improved convergence rate for the approximate eigenvalues, namely Ο(h). This result is confirmed by model numerical experiments. © Springer-Verlag Berlin Heidelberg 2006.