Abstract
Two extended numerical differentiation methods based on Green's second identity are presented. These may be used for postprocessing approximate solutions in general material distributions, including inhomogeneous and discontinuous 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, analytically known configurations. The singularities encountered in the necessary integral kernels for second derivatives are evaluated using finite part integration techniques. Both methods are illustrated by numerical experiments, and results are shown for differentiation of quasi-harmonic functions in inhomogeneous domains. Copyright © 2000 John Wiley & Sons, Ltd.
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