This work investigates the isoparametric upwind discontinuous Galerkin method for solving the radiation transport equation defined on a bounded domain $D$ with a piecewise $C^{ k+1}$ smooth curved boundary. An auxiliary mapping is constructed to approximate the original curved domain. The analysis delineates a high-order optimal convergence rate under the DG norm, which comprehensively balances the errors stemming from the numerical discretization and the geometric approximation. Two- and three-dimensional numerical experiments validate the theoretical results.
Categories: math.NA cs.NA