An adaptive approach to variational nodal diffusion problems

An adaptive grid method is presented for the solution of neutron diffusion problems in two dimensions. The primal hybrid finite elements employed in t he variational nodal method are used to reduce the diffusion equation to a coupled set of elemental response matrices. An a posteriori error estimator is developed to indicate the magnitude of local errors stemming from the l ow-order elemental interface approximations. An iterative procedure is impl emented in which p refinement is applied locally by increasing the polynomi al order of the interface approximations. The automated algorithm utilizes the a posteriori estimator to achieve local error reductions until an accep table level of accuracy is reached throughout the problem domain. Applicati on to a series of X-Y benchmark problems indicates the reduction of computa tional effort achievable by replacing uniform with adaptive refinement of t he spatial approximations.