Constructive Approximation

, Volume 41, Issue 1, pp 1–22 | Cite as

A Bernstein–Bézier Basis for Arbitrary Order Raviart–Thomas Finite Elements

Article

Abstract

A Bernstein–Bézier basis is developed for \({\varvec{H}}({{\mathrm{div}}})\)-conforming finite elements that gives a clear separation between the curls of the Bernstein basis for the polynomial discretization of the space \(H^1\), and the noncurls that characterize the specific \({\varvec{H}}({{\mathrm{div}}})\) finite element space (Raviart–Thomas in our case). The resulting basis has two distinct components reflecting this separation with the basis functions in each component having a natural identification with a domain point, or node, on the element. It is shown that the basis retains the favorable properties of the Bernstein basis that were used in Ainsworth et al. (SIAM J Sci Comput 3087–3109, 2011) to develop efficient computational procedures for the application of the elements.

Keywords

Spectral/\(hp\) finite element Bernstein polynomials  \({\varvec{H}}({{\mathrm{div}}})\) finite elements Sum-factorisation Raviart–Thomas space Maxwell eigenvalue problem 

Mathematics Subject Classification

65N30 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Mark Ainsworth
    • 1
  • Gaelle Andriamaro
    • 2
  • Oleg Davydov
    • 3
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of Mathematics and StatisticsStrathclyde UniversityGlasgowScotland, UK
  3. 3.Department of MathematicsUniversity of GiessenGiessenGermany

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