Extracting edge flux intensity functions for the Laplacian

The solution to the Laplace operator in three-dimensional domains in the vicinity of straight edges is presented as an asymptotic expansion involving eigenpairs with their coe@cients called edge +ux intensity functions (EFIFs). The eigenpairs are identical to their two-dimensional counterparts over a plane perpendicular to the edge. Extraction of EFIFs however, cannot be obtained in a straightforward manner over this two-dimensional plane. A method based on L2 projection and Richardson extrapolation is presented for point-wise extraction of EFIFs from p-Bnite element solutions and illustrated by examples. A similar but more e@cient method, based on ‘energy projection’, for extracting EFIFs is proposed