Differentiation of finite element approximations to harmonic functions (EM field computation)

Derivatives of finite-element solutions are essential for most postprocessing operations, but numerical differentiation is an error-prone process. High-order derivatives of harmonic functions can be computed accurately by a technique based on Green's second identity, even where the finite element solution itself has insufficient continuity to possess the desired derivatives. Data are presented on the sensitivity of this method to solution error as well as to the numerical quadratures used. The procedure is illustrated by application to finding second and third derivatives of a first-order finite-element solution.