ARBITRARY-ORDER DISCONTINUOUS GALERKIN DISCRETIZATION FOR SN TRANSPORT USING POLYGONAL BERNSTEIN-BéZIER FUNCTIONS

摘要

In this work, we present an arbitrary-order discontinuous Galerkin finite element discretization of the SN transport equation on 2D polygonal grids using Bernstein-B′ezierfunctions. For a polynomial order of p, these functions span the {x~ay~b}(a+b)≤p space offunctions with a dimension of pn + (p-1)(p-2)/2 for a polygonal element with n vertices. Afour-step process is presented to construct the basis functions. Numerical tests confirmthat the functions capture exactly monomial solutions and appropriate convergence ratesare observed. A final example demonstrates that the functions provide full resolution inthe thick diffusion limit.