Bernstein–Bézier finite elements of arbitrary order and optimal assembly procedures

Mark Ainsworth, Miangaly Gaelle Andriamaro, Oleg Davydov

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

Algorithms are presented that enable the element matrices for the standard finite element space, consisting of continuous piecewise polynomials of degree $n$ on simplicial elements in $\mathbb{R}^d$, to be computed in optimal complexity $\mathcal{O}(n^{2d})$. The algorithms (i) take into account numerical quadrature; (ii) are applicable to nonlinear problems; and (iii) do not rely on precomputed arrays containing values of one-dimensional basis functions at quadrature points (although these can be used if desired). The elements are based on Bernstein polynomials and are the first to achieve optimal complexity for the standard finite element spaces on simplicial elements.
LanguageEnglish
Pages3087-3109
Number of pages23
JournalSIAM Journal on Scientific Computing
Volume33
Issue number6
Early online date1 Nov 2011
DOIs
Publication statusPublished - 2011

Fingerprint

Bézier
Polynomials
Finite Element
Numerical Quadrature
Bernstein Polynomials
Piecewise Polynomials
Arbitrary
Quadrature
Basis Functions
Nonlinear Problem
Standards

Keywords

  • finite elements
  • optimal assembly
  • polynomials

Cite this

Ainsworth, Mark ; Andriamaro, Miangaly Gaelle ; Davydov, Oleg. / Bernstein–Bézier finite elements of arbitrary order and optimal assembly procedures. In: SIAM Journal on Scientific Computing. 2011 ; Vol. 33, No. 6. pp. 3087-3109.
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Bernstein–Bézier finite elements of arbitrary order and optimal assembly procedures. / Ainsworth, Mark; Andriamaro, Miangaly Gaelle; Davydov, Oleg.

In: SIAM Journal on Scientific Computing, Vol. 33, No. 6, 2011, p. 3087-3109.

Research output: Contribution to journalArticle

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AU - Andriamaro, Miangaly Gaelle

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