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The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

The Department also includes the iSchool Research Group, which performs leading research into socio-technical phenomena and topics such as information retrieval and information seeking behaviour.

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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.