Differentiation of finite element solutions to non-linear problems

Two extended numerical differentiation methods based on Green's second iden tity are presented. These may be used for postprocessing approximate soluti ons in general material distributions, including inhomogeneous and disconti nuous material characteristics. The first method uses a general formulation with Green's functions and extended Poisson kernels for standard domains, while the second applies Green's functions to certain restricted, analytica lly known configurations. The singularities encountered in the necessary in tegral kernels for second derivatives are evaluated using finite part integ ration techniques. Both methods are illustrated by numerical experiments, a nd results are shown for differentiation of quasiharmonic functions in inho mogeneous domains. Copyright (C) 2000 John Wiley & Sons, Ltd.