Supercloseness between the elliptic projection and the approximate eigenfunction and its application to a postprocessing of finite element eigenvalue problems

Authors:
Andrey B. Andreev
Affiliations:
Technical University of Gabrovo & IPP – Bulgarian Academy of Sciencies
Venue:
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Year:
2004

Citing 2
Cited 0

Ultraconvergence of the patch recovery technique

Mathematics of Computation
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)

Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)

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Abstract

An estimate confirming the supercloseness between the Ritz projection and the corresponding eigenvectors, obtained by finite element method, is hereby proved. This result is true for a large class of self-adjoint 2m–order elliptic operators. An application of this theorem to the superconvergence postprocessing patch-recovery technique for finite element eigenvalue problems is also presented. Finally, the theoretical investigations are supported by numerical experiments.