Progress in differentiation of approximate data

Accurate derivative calculation is a key process in computational electromagnetics. Differentiation is required for graphic display, a posteriori error estimation, automatic mesh refinement, and result post-processing. The choice of method depends on the accuracy required, and on the order of derivatives to be computed. This paper reviews recent progress, and compares several recent derivative-extraction methods: local smoothing, superconvergent-patch recovery (SPR), and methods based on Green´s second identity. The SPR approach of Zhu and Zienkiewicz (see Finite Elements in Analysis and Design, vol.19, p.1123, 1995) has been extended in several ways to yield good accuracy at low cost, but it can only produce first derivatives. The Green´s identity methods of Silvester and Omeragic (see International Journal of Applied Electomagnetics in Materials, vol.4, p.123-136, 1993) are computationally expensive, but extremely accurate, even for third and fourth derivatives. Representative numerical results illustrate the methods discussed