This paper presents a hp−refinement method for a first order scalar transportreaction equation discretized by a discontinuous Galerkin method. First, the theoretical rates of convergence of h− and p−refinement are recalled and numerically tested. Then, in order to design some meshes, we propose two different estimators of the local error on the spatial domain. These quantities are analysed and compared depending on the regularity of the solution so as to find the best way to lead the refinement

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... process and the best strategy to choose between h− and p−refinement. Finally, the different possible refinement strategies are compared first on analytical examples and then on realistic applications for neutron transport in a nuclear reactor core.