Progress in differentiation of approximate data

IEEE Antennas and Propagation Magazine

Volumn 38, Issue 1, 1996, Pages 25-30

  Orneragic, Dzevat ^a   Silvester, Peter P ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CALCULATIONS; COMPUTATIONAL METHODS; DIFFERENTIATION (CALCULUS); FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; INTERPOLATION; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS;

DERIVATIVE EXTRACTION METHODS; LOCAL SMOOTHING; SUPERCONVERGENT PATCH RECOVERY;

ELECTROMAGNETIC FIELD THEORY;

EID: 0030081749     PISSN: 10459243     EISSN: None     Source Type: Journal    
DOI: 10.1109/74.491288     Document Type: Article

References (18)

1. B. Szabo and I. Babuska, Finite Element Analysis, New York, John Wiley, 1991.
2. M. Krizek and P. Neittaanmäki, "On superconvergence techniques," Acta Applicandae Mathematicae, 9, 1987, pp. 175-198.
3. G. Goodsell and H. R. Whiteman, "A unified treatment of superconvergence recovered gradient functions for piecewise linear finite element approximations," International Journal for Numerical Methods in Engineering, 27, 1989, pp. 469-481.
4. M. Krizek, "Superconvergence phenomena in the finite element method," Computer Methods in Applied Mechanics and Engineering, 116, 1994, pp. 157-163.
5. D. M. Hawken, P. Townsend, and M. F. Webster, "A comparison of gradient recovery methods in finite-element calculations," Communications in Applied Numerical Methods, 7, 1991, pp. 195-204.
6. N. E. Wiberg and F. Abdulwahab, "Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions," International Journal for Numerical Methods in Engineering, 37, 1994, pp. 3417-3440.
7. O. C. Zienkiewicz and J. Z Zhu, "Superconvergence and superconvergent patch recovery," Finite Elements in Analysis and Design, 19, 1995, pp. 1123.
8. P. P. Silvester and D. Omeragic, "A comparative experimental study of differentiation on finite elements," International Journal of Applied Electromagnetics in Materials, 1993, pp. 123-136.
9. P. P. Silvester and D. Omeragic, "A two-dimensional Zhu-Zienkiewicz method for gradient recovery from finite element solutions," COMPEL, 12, 1993, pp. 191-204.
10. O. C. Zienkiewicz and J. Z. Zhu, "The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique," International Journal for Numerical Methods in Engineering, 33, 1992, pp. 1331-1364.
11. D. Omeragic and P. P. Silvester, "Numerical differentiation in magnetic field postprocessing," International Journal of Numerical Modelling, 1995, (in press).
12. H. Ohtsubo and M. Kitamura, "Element by element a posteriori error estimation of the finite element analysis for three-dimensional elastic problems," International Journal for Numerical Methods in Engineering, 33, 1992, pp. 1755-1769.
13. P. P. Silvester, "Differentiation of finite element approximations to harmonic functions," IEEE Transactions on Magnetics, MAG-27, 1991, pp. 3774-3779.
14. D. Qmeragic and P. P. Silvester, "Numerical differentiation of harmonic functions in axisymmetric coordinates," IEEE Transactions on Magnetics, MAG-31, 1995, (in press).
15. P. P. Silvester and D. Omeragic, "Differentiation of finite element solutions of the Poisson equation," IEEE Transactions on Magnetics, MAG-29, 1993, pp. 1993-1996.
16. D. Omeragic and P. P. Silvester, "Differentiation of approximate solutions of the Helmholtz equation," International Journal of Applied Electromagnetics in Materials, 5, 1994, pp. 137-147.
17. D. Omeragic and P.P. Silvester, "Singular and near-singular integrals in high-precision derivative computation," COMPEL, 13, 1995, (in press).
18. I. Babuska and A. Miller, "The post-processing approach in the finite element method-Part 2: The calculation of stress intensity factors," International Journal for Numerical Methods in Engineering, 20, 1984, pp. 1111-1129.