Arbitrary-Order Bernstein–Bézier Functions for DGFEM Transport on 3D Polygonal Grids

In this paper, we present an arbitrary-order discontinuous Galerkin finite element discretization of the SN transport equation on 3D extruded polygonal prisms. Basis functions are formed by the tensor product of 2D polygonal Bernstein–Bézier functions and 1D Lagrange polynomials. For a polynomial degree p, these functions span {xayb}(a+b)≤p⊗{zc}c∈(0,p) with a dimension of np(p+1)+(p+1)(p−1)(p−2)/2 on an extruded n-gon. Numerical tests confirm that the functions capture exactly monomial solutions, achieve expected convergence rates, and provide full resolution in the thick diffusion limit.