Error Analysis of the Nodal Expansion Method for Solving the Neutron Diffusion Equation

An error analysis is presented of the quartic polynomial nodal expansion method for solving the one-dimensional, neutron diffusion equation that originates from employing the transverse integration technique. Error bound expressions are determined for the L∞ error norms associated with the nodal surface flux and various moments of the nodal flux. Employing several test problems, these global error bounds were found to be conservative, but not excessively, in bounding the true errors Utilizing a functional form of the local error estimate for the node average flux, it is shown that a mesh-doubling technique can be effectively utilized to estimate the required cell size for uniform mesh refinement to achieve a specified global error fidelity. When employed in conjunction with a multigrid acceleration technique, this provides the foundations upon which to develop an adaptive spatial mesh algorithm.