An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
Boundary value problems for transport equations
Boundary value problems for transport equations
Mathematical methods in image reconstruction
Mathematical methods in image reconstruction
Chebyshev Spectral Methods for Radiative Transfer
SIAM Journal on Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Cubature over the sphere S2 in Sobolev spaces of arbitrary order
Journal of Approximation Theory
Chebyshev spectral-SN method for the neutron transport equation
Computers & Mathematics with Applications
Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation
Journal of Computational Physics
Spatial Multigrid for Isotropic Neutron Transport
SIAM Journal on Scientific Computing
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
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The radiative transfer equation (RTE) occurs in a wide variety of applications. In this paper, we study discrete-ordinate discontinuous Galerkin methods for solving the RTE. The numerical methods are formed in two steps. In the first step, the discrete ordinate technique is applied to discretize the integral operator for the angular variable, resulting in a semidiscrete hyperbolic system. In the second step, the spatial discontinuous Galerkin method is applied to discretize the semidiscrete system. A stability and error analysis is performed on the numerical methods. Some numerical examples are included to demonstrate the convergence behavior of the methods.