A Zienkiewicz-type finite element applied to fourth-order problems

Authors:
A. B. Andreev;M. R. Racheva
Affiliations:
Department of Informatics, Technical University of Gabrovo, Gabrovo and IPP-BAS, Sofia, Bulgaria;Department of Mathematics, Technical University of Gabrovo, Gabrovo, Bulgaria
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 3
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Abstract

This paper deals with convergence analysis and applications of a Zienkiewicz-type (Z-type) triangular element, applied to fourth-order partial differential equations. For the biharmonic problem we prove the order of convergence by comparison to a suitable modified Hermite triangular finite element. This method is more natural and it could be applied to the corresponding fourth-order eigenvalue problem. We also propose a simple postprocessing method which improves the order of convergence of finite element eigenpairs. Thus, an a posteriori analysis is presented by means of different triangular elements. Some computational aspects are discussed and numerical examples are given.