BIT Numerical Mathematics

, Volume 54, Issue 2, pp 469–484

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

Article

DOI: 10.1007/s10543-013-0462-0

Cite this article as:
Lamichhane, B.P. Bit Numer Math (2014) 54: 469. doi:10.1007/s10543-013-0462-0

Abstract

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.

Keywords

Biharmonic equationClamped boundary conditionsStrang’s lemmaNonconforming methodA priori estimateBiorthogonal system

Mathematics subject classification (2010)

65D1565L6041A15

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

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