Computation of Electrostatic Field near Three-Dimensional Corners and   Edges
  Theoretically, the electric field becomes infinite at corners of two and three dimensions and edges of three dimensions. Conventional finite-element and boundary element methods do not yield satisfactory results at close proximity to these singular locations. In this paper, we describe the application of a fast and accurate BEM solver (which usesexact analytic expressions to compute the effect of source distributions on flatsurfaces) to compute the electric field near three-dimensional corners and edges. Results have been obtained for distances as close as 1$\mu m$ near the corner/edge and good agreement has been observed between the present results and existing analytical solutions. 
N. Majumdar, S. Mukhopadhyay