hp-mesh adaptation for 1-D multigroup neutron diffusion problems

In this work, we propose, implement and test two fully automated mesh adaptation methods for 1-D multigroup eigenproblems. The first method is the standard hp-adaptive refinement strategy and the second technique is a goal-oriented hp-adaptive refinement strategy. The hp-strategies deliver optimal guaranteed solutions obtained with exponential convergence rates with respect to the number of unknowns. The goal-oriented method combines the standard hp-adaptation technique with a goal-oriented adaptivity based on the simultaneous solution of an adjoint problem in order to compute quantities of interest, such as reaction rates in a sub-domain or point-wise fluxes or currents. These algorithms are tested for various multigroup 1-D diffusion problems and the numerical results confirm the optimal, exponential convergence rates predicted theoretically