A posteriori error estimation for the one-dimensional arbitrarily high-order transport-nodal method

An a posteriori error analysis of the spatial approximation is developed for the one-dimensional Arbitrarily High-Order Transport-Nodal method. The error estimator, based on the L2 norm of the error, preserves the order of the convergence of the method when the mesh size tends to zero. The proposed error estimator is decomposed into error indicators to allow the quantification of local errors. A simple test problem with isotropic scattering is solved to compare the behavior of the true errors with the estimated errors.