PROGRESS IN DIFFERENTIATION OF APPROXIMATE DATA

Accurate derivative calculation is a key process in computational elec tromagnetics. Differentiation is required for graphic display, a poste riori error estimation, automatic mesh refinement, and result post-pro cessing. The choice of method depends on the accuracy required, and on the order of derivatives to be computed. This paper reviews recent pr ogress, and compares several recent derivative-extraction methods: loc al smoothing, superconvergent-patch recovery (SPR), and methods based on Green's second identity. The SPR approach of Zhu and Zienkiewicz ha s been extended in several ways to yield good accuracy at low cost, bu t it can only produce first derivatives. The Green's identity methods of Silvester and Omeragic are computationally expensive, but extremely accurate, even for third and fourth derivatives. Representative numer ical results illustrate the methods discussed.