Adaptive approach to variational nodal diffusion problems

Hui Zhang, E. E. Lewis

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


An adaptive grid method is presented for the solution of neutron diffusion problems in two dimensions. The primal hybrid finite elements employed in the 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 low-order elemental interface approximations. An iterative procedure is implemented in which p refinement is applied locally by increasing the polynomial order of the interface approximations. The automated algorithm utilizes the a posteriori estimator to achieve local error reductions until an acceptable level of accuracy is reached throughout the problem domain. Application to a series of X-Y benchmark problems indicates the reduction of computational effort achievable by replacing uniform with adaptive refinement of the spatial approximations.

Original languageEnglish (US)
Pages (from-to)14-22
Number of pages9
JournalNuclear Science and Engineering
Issue number1
StatePublished - Jan 2001

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


Dive into the research topics of 'Adaptive approach to variational nodal diffusion problems'. Together they form a unique fingerprint.

Cite this