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Hierarchical High Order Finite Element Approximation Spaces for H(div) and H(curl)

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Denise De Siqueira

    (Unicamp, IMECC)

  • Philippe R. B. Devloo

    (Unicamp, FEC)

  • Sônia M. Gomes

    (Unicamp, IMECC)

Abstract

The aim of this paper is to present a systematic procedure for the construction of a hierarchy of high order finite element approximations for H(div) and H(curl) spaces based on quadrilateral and triangular elements with rectilinear edges. The principle is to chose appropriate vector fields, based on the geometry of each element, which are multiplied by an available set of H 1 hierarchical scalar basic functions. We show that the resulting local vector bases can be combined to obtain continuous normal or tangent components on the elements interfaces, properties that characterize piecewise polynomial functions in H(div) or H(curl), respectively.

Suggested Citation

  • Denise De Siqueira & Philippe R. B. Devloo & Sônia M. Gomes, 2010. "Hierarchical High Order Finite Element Approximation Spaces for H(div) and H(curl)," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 269-276, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_28
    DOI: 10.1007/978-3-642-11795-4_28
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