Error Analysis of a Finite Element-Integral Equation Scheme for Approximating the Time-Harmonic Maxwell System

In 1996 Hazard and Lenoir suggested a variational formulation of Maxwell's equations using an overlapping integral equation and volume representation of the solution [SIAM J. Math. Anal., 27 (1996), pp. 1597-1630]. They suggested a numerical scheme based on this approach, but no error analysis...

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Veröffentlicht in:	SIAM journal on numerical analysis 2003-01, Vol.40 (1), p.198-219
Hauptverfasser:	Hsiao, G. C., Monk, P. B., N. Nigam
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied classical electromagnetism Boundary conditions Discrete problems Electric fields Electromagnetic wave propagation, radiowave propagation Electromagnetism electron and ion optics Error analysis Exact sciences and technology Finite element method Fundamental areas of phenomenology (including applications) Mathematical vectors Mathematics Maxwell equations Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Physics Polynomials Sciences and techniques of general use Tetrahedrons
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Beschreibung
Zusammenfassung:	In 1996 Hazard and Lenoir suggested a variational formulation of Maxwell's equations using an overlapping integral equation and volume representation of the solution [SIAM J. Math. Anal., 27 (1996), pp. 1597-1630]. They suggested a numerical scheme based on this approach, but no error analysis was provided. In this paper, we provide a convergence analysis of an edge finite element scheme for the method. The analysis uses the theory of collectively compact operators. Its novelty is that a perturbation argument is needed to obtain error estimates for the solution of the discrete problem that is best suited for implementation.
ISSN:	0036-1429 1095-7170