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Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. (English) Zbl 1237.65120
The authors derive finite element spaces by using Bernstein-Bézier polynomials of arbitrary order. The features of the algorithms presented by the authors are applicable to nonlinear problems and do not rely on precomputed arrays containing values of one-dimensional basis functions at quadrature points. Numerous examples using Bernstein-Bézier polynomials are presented, e.g. prismatic Bernstein-Bézier finite element, quadrilateral Bernstein-Bézier finite element, and hexahedral Bernstein-Bézier finite element.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J60 Nonlinear elliptic equations
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