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

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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.

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Acknowledgments

I am grateful to the anonymous referees for their valuable suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia

    Bishnu P. Lamichhane

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  1. Bishnu P. Lamichhane
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Correspondence to Bishnu P. Lamichhane.

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Communicated by Ragnar Winther.

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Lamichhane, B.P. A finite element method for a biharmonic equation based on gradient recovery operators. Bit Numer Math 54, 469–484 (2014). https://doi.org/10.1007/s10543-013-0462-0

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  • DOI: https://doi.org/10.1007/s10543-013-0462-0

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