Spectral Methods for Axisymmetric Domains

by Christine Bernardi, Monique Dauge, Yvon Maday

Paperback. This book is devoted to the mathematical and numerical analysis of partial differential equations set in a three-dimensional axisymmetric domain, that is a domain generated by rotation of a bidimensional meridian domain around an axis. Thus a three dimensional axisymmetric domain boundary value problem can be reduced to a countable family of two-dimensional equations, by expanding the data and unknowns in Fourier series, and an infinite-order approximation is obtained by truncating the Fourier series. We first present the functional framework for this family of we fully characterize the special weighted spaces on the meridian domain associated with the Fourier coefficients of functions belonging to standard three-dimensional Sobolev spaces. Then starting from a well-posed three-dimensional problem, we write each two-dimensional equation in variational form and prove its well-posedness. When the meridian domain is polygonal, we desc

Paperback

Published January 1, 1999