Pyramid Algorithms for Bernstein-Bézier Finite Elements of High, Nonuniform Order in Any Dimension

  title={Pyramid Algorithms for Bernstein-B{\'e}zier Finite Elements of High, Nonuniform Order in Any Dimension},
  author={Mark Ainsworth},
  journal={SIAM J. Sci. Comput.},
  • M. Ainsworth
  • Published 27 March 2014
  • Computer Science
  • SIAM J. Sci. Comput.
The archetypal pyramid algorithm is the de Casteljau algorithm, which is a standard tool for the evaluation of Bezier curves and surfaces. Pyramid algorithms replace an operation on a single high order polynomial by a recursive sequence of self-similar affine combinations, and are ubiquitous in computer aided geometric design for computations involving high order curves and surfaces. Pyramid algorithms have received no attention whatsoever from the high (or low) order finite element community… 

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