BIT Numerical Mathematics

, Volume 54, Issue 2, pp 469–484

A finite element method for a biharmonic equation based on gradient recovery operators



A new non-conforming finite element method is proposed for the approximation of the biharmonic equation with clamped boundary condition. The new formulation is based on a gradient recovery operator. Optimal a priori error estimates are proved for the proposed approach. The approach is also extended to cover a singularly perturbed problem.


Biharmonic equation Clamped boundary conditions Strang’s lemma Nonconforming method A priori estimate Biorthogonal system 

Mathematics subject classification (2010)

65D15 65L60 41A15 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia

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