Multi-\textbf{hp} adaptive discontinuous Galerkin methods for simplified \(P_{N}\) approximations of 3D radiative transfer in non-gray media (Q2301293)

The authors present a multi-\(hp\) adaptive discontinuous Galerkin method for 3D simplified \(P_{N}\) approximations of radiative transfer in non-gray media capable of reaching accuracies superior to most of the methods in the literature. They propose a class of high-order adaptive discontinuous Galerkin methods using space error estimators. The proposed method is able to solve problems where 3D meshes contain finite elements of different kind with the number of equations and polynomial orders of approximation varying locally on the finite element edges, faces, and interiors. The proposed method has also the potential to perform both isotropic and anisotropic adaptation for each band in the optical spectrum. Several numerical results are presented to illustrate the performance of the proposed method for 3D radiative simulations. The computed results confirm its capability to solve 3D simplified \(P_{N}\) approximations of radiative transfer in non-gray media.