Error Analysis of a Finite Element-Integral Equation Scheme for Approximating the Time-Harmonic Maxwell System
Date
2002
Authors
Hsiao, George C.
Monk, Peter B.
Nigam, N.
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
In 1996 Hazard and Lenoir suggested a variational formulation of Maxwell's equations
using an overlapping integral equation and volume representation of the solution. 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. It's 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.