Numerical analysis of a model for an axisymmetric guide for electromagnetic waves - Part I: The continuous problem and its Fourier expansion

As a first model for an electromagnetic wave guide, we consider Maxwell's system in a three-dimensional axisymmetric domain provided with appropriate boundary conditions on different parts of the boundary. We check the well-posedness of the corresponding variational problem. We write the Fourier expansion of the solution as a function of the angular variable and derive the well-posedness of the two-dimensional problems satisfied by each Fourier coefficient. The first step for approximating the three-dimensional solution relies on Fourier truncation, and we prove optimal estimates for the error issued from this truncation. Copyright (c) 2005 John Wiley & Sons, Ltd.