Accurate computation of local and global electrostatic quantities from FE solutions

In this paper we present a numerical post processing procedure, based on Poisson integrals, which allows a more accurate computation of local and global electrostatic quantities, such as electrical fields, charge densities and capacitances starting from rough Finite Element (FE) solutions to 2D and 3D electrostatic problems, governed by Laplace and Poisson equations. Some examples of application of the proposed postprocessing procedure to the FE solutions of 3D electrostatic problems are also provided. The additional computational cost is negligible if compared with the achievable increase of accuracy.