期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 33, 期 6, 页码 3087-3109出版社
SIAM PUBLICATIONS
DOI: 10.1137/11082539X
关键词
spectral/hp finite element; Bernstein polynomials
资金
- Engineering and Physical Sciences Research Council of Great Britain [EP/G036136/1]
- SORSAS
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 R(d), to be computed in optimal complexity 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.
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