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

Authors:
A. B. Andreev;R. D. Lazarov;M. R. Racheva
Affiliations:
Department of Applied Informatics, Technical University of Gabrovo, Bulgaria;Department of Mathematics, Texas A&M University, 3368-TAMU, College Station, TX;Department of Computational Mathematics, Chalmers University of Technology, Sweden
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 5
Cited 0

Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
The symmetric eigenvalue problem

The symmetric eigenvalue problem
A two-grid discretization scheme for eigenvalue problems

Mathematics of Computation
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Finite Element Method for Elliptic Problems
A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems

SIAM Journal on Numerical Analysis

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Abstract

A new procedure for accelerating the convergence of mixed finite element approximations of the eigenpairs and of the biharmonic operator is proposed. It is based on a postprocessing technique that involves an additional solution of a source problem on an augmented finite element space. This space could be obtained either by substantially refining the grid, the two-grid method, or by using the same grid but increasing the order of polynomials by one, the two-space method. The numerical results presented and discussed in the paper illustrate the efficiency of the postprocessing method.