Spectral methods for axisymmetric domains Book

Hardbound. 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 equations: 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