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

Ainsworth, Mark and Andriamaro, Miangaly Gaelle and Davydov, Oleg (2011) Bernstein–Bézier finite elements of arbitrary order and optimal assembly procedures. SIAM Journal on Scientific Computing, 33 (6). pp. 3087-3109. ISSN 1064-8275

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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.

Item type: Article
ID code: 36314
Keywords: finite elements , optimal assembly , polynomials, Probabilities. Mathematical statistics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 05 Dec 2011 14:41
    Last modified: 12 Mar 2012 11:42
    URI: http://strathprints.strath.ac.uk/id/eprint/36314

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