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

Authors:
Andrey Andreev;Raytcho Lazarov;Milena Racheva
Affiliations:
Department of Informatics, Technical University of Gabrovo, Gabrovo, Bulgaria;Department of Mathematics, Texas A & M University, College Station, TX;Department of Mathematics, Technical University of Gabrovo, Gabrovo, Bulgaria
Venue:
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Year:
2005

Citing 2
Cited 0

A two-grid discretization scheme for eigenvalue problems

Mathematics of Computation
Postprocessing and higher order convergence of the mixed finite element approximations of biharmonic eigenvalue problems

Journal of Computational and Applied Mathematics

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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 O(h1/2) for the eigenvalues and the eigenfunctions was established. Using postprocessing we derive an improved convergence rate for the approximate eigenvalues, namely O(h). This result is confirmed by model numerical experiments.