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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method. II. The discrete problem
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by A. Bendali PDF
Math. Comp. 43 (1984), 47-68 Request permission

Abstract:

With the help of curved and mixed finite elements, we introduce an approximate surface on which the discrete problem is defined and construct surface currents and charges which approximate the solution of the continuous problem studied in a previous part. We study the existence and uniqueness of the solution of the discrete problem and give estimates for the error between currents, charges, corresponding fields and their calculated approximations.
References
  • Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
  • F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 8 (1974), no. R-2, 129–151 (English, with French summary). MR 365287
  • Yvonne Choquet-Bruhat, Cecile DeWitt-Morette, and Margaret Dillard-Bleick, Analysis, manifolds and physics, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. MR 0467779
  • Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
  • G. J. Fix and R. A. Nicolaides, An analysis of mixed finite element approximations for periodic acoustic wave propagation, SIAM J. Numer. Anal. 17 (1980), no. 6, 779–786. MR 595443, DOI 10.1137/0717065
  • Tuong Ha Duong, A finite element method for the double-layer potential solutions of the Neumann exterior problem, Math. Methods Appl. Sci. 2 (1980), no. 2, 191–208. MR 570403, DOI 10.1002/mma.1670020206
  • R. F. Harrington, "Characteristic modes for antennas and scatterers," Numerical and Asymptotic Techniques in Electromagnetics (R. Mittra, ed.), Topics in Applied Physics, Vol. 3, Springer-Verlag, Berlin, Heidelberg, New York, 1975.
  • G. C. Hsiao and W. L. Wendland, The Aubin-Nitsche lemma for integral equations, J. Integral Equations 3 (1981), no. 4, 299–315. MR 634453
  • J. Giroire, Integral Equation Methods for Exterior Problems for the Helmholtz Equation, Rapport Interne no. 40, Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, 1978.
  • J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
  • J. Nečas, Les Méthodes Directes en Théorie des Équations Elliptiques, Masson, Paris and Academia, Prague, 1967.
  • J.-C. Nédélec, Curved finite element methods for the solution of singular integral equations on surfaces in $R^{3}$, Comput. Methods Appl. Mech. Engrg. 8 (1976), no. 1, 61–80. MR 455503, DOI 10.1016/0045-7825(76)90053-0
  • J.-C. Nédélec, Computation of eddy currents on a surface in $\textbf {R}^{3}$ by finite element methods, SIAM J. Numer. Anal. 15 (1978), no. 3, 580–594. MR 495761, DOI 10.1137/0715038
  • D. T. Paris & F. K. Hurd, Basic Electromagnetic Theory, McGraw-Hill, Physical and Quantum Electronic Series, McGraw-Hill, New York, 1969. D. J. Poggio & E. K. Miller, "Solutions of three-dimensional scattering problems," Computer Techniques for Electromagnetics (R. Mittra, ed.), Pergamon Press, New York, 1973. S. S. M. Rao, D. R. Wilton & A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas and Propagation, v. AP-30, 1982, pp. 409-418.
  • P.-A. Raviart and J. M. Thomas, A mixed finite element method for 2nd order elliptic problems, Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975) Lecture Notes in Math., Vol. 606, Springer, Berlin, 1977, pp. 292–315. MR 0483555
  • Franz Rellich, Über das asymptotische Verhalten der Lösungen von $\Delta u+\lambda u=0$ in unendlichen Gebieten, Jber. Deutsch. Math.-Verein. 53 (1943), 57–65 (German). MR 17816
  • J. M. Thomas, Sur l’Analyse Numérique des Méthodes d’Eléments Finis Hybrides et Mixtes, Thèse de Doctorat d’Etat, Univ. Paris VI, 1977. J. M. Thomas, Méthodes d’Éléments Finis Mixtes et Hybrides, Cours de D. E. A. 1980-1981, Univ. Paris VI, Laboratoire d’Analyse Numérique (LA 189), 1981.
  • François Trèves, Introduction to pseudodifferential and Fourier integral operators. Vol. 2, University Series in Mathematics, Plenum Press, New York-London, 1980. Fourier integral operators. MR 597145, DOI 10.1007/978-1-4684-8780-0
  • J. Van Bladel, Electromagnetic Fields, McGraw-Hill, New York, 1964.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 43 (1984), 47-68
  • MSC: Primary 65N30; Secondary 78-08, 78A45
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0744924-3
  • MathSciNet review: 744924