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… (More)

A Bernstein-Bézier basis is developed for H(div)-conforming finite elements that gives a clear separation between the curls of the Bernstein basis for the polynomial discretisation of the space H1, and the non-curls that characterize the specific H(div) finite element space (Raviart-Thomas in our case). The resulting basis has two distinct components… (More)