Bernstein-Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures

@article{Ainsworth2011BernsteinBzierFE,
  title={Bernstein-B{\'e}zier Finite Elements of Arbitrary Order and Optimal Assembly Procedures},
  author={Mark Ainsworth and Gaelle Andriamaro and Oleg Davydov},
  journal={SIAM J. Scientific Computing},
  year={2011},
  volume={33},
  pages={3087-3109}
}
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, to be computed in optimal complexity O(n). The algorithms (i) take account of numerical quadrature; (ii) are applicable to non-linear problems; and, (iii) do not rely on pre-computed arrays containing values of one-dimensional basis functions at quadrature points (although these can be used if desired). The… CONTINUE READING