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A Mixed Finite Element Method for the Biharmonic Problem Using Biorthogonal or Quasi-Biorthogonal Systems

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Abstract

We consider a finite element method based on biorthogonal or quasi-biorthogonal systems for the biharmonic problem. The method is based on the primal mixed finite element method due to Ciarlet and Raviart for the biharmonic equation. Using different finite element spaces for the stream function and vorticity, this approach leads to a formulation only based on the stream function. We prove optimal a priori estimates for both stream function and vorticity, and present numerical results to demonstrate the efficiency of the approach.

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Authors and Affiliations

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

    Bishnu P. Lamichhane

  2. Mathematical Sciences Institute, Australian National University, ACT 0200, Canberra, 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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Lamichhane, B.P. A Mixed Finite Element Method for the Biharmonic Problem Using Biorthogonal or Quasi-Biorthogonal Systems. J Sci Comput 46, 379–396 (2011). https://doi.org/10.1007/s10915-010-9409-7

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  • DOI: https://doi.org/10.1007/s10915-010-9409-7

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