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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Bibliographic Details
Published in:SIAM journal on numerical analysis Vol. 40; no. 1; pp. 198 - 219
Main Authors: Hsiao, G. C., Monk, P. B., N. Nigam
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2003
Subjects:
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
Convergence of numerical methods
Electromagnetism
Error estimation
Edge finite element
Partial differential equation
Fredholm equation
Scattering theory
Finite element method
Compact operator
Numerical analysis
Maxwell equation
Integral representation
Mathematical physics
ISSN:0036-1429
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Summary: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