Differentiation of finite-element solutions of the Poisson equation

A technique, based on Green´s second identity, is developed for accurate computation of first and second derivatives of potential functions in fields governed by Poisson´s equation. The method is not sensitive to data error, and derivatives can be computed to an accuracy at least comparable to that of the potential itself. In C0-continuous finite-element solutions, where second derivatives do not exist, several correct significant figures are still available in the second derivatives. Test data are presented on the sensitivity to solution error as well as the numerical quadrature used. The procedure is illustrated by finding first and second derivatives of a first-order finite-element solution of Poisson´s equation in a square region.