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 coefficients called edge flux 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-finite element solutions and illustrated by examples. A similar but more efficient method, based on 'energy projection', for extracting EFIFs is proposed.