A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain
Journal article, 2021

We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems.

Weighted Sobolev Space

Fourier Truncation

Axisymmetric Domain

Stokes Equations


Niklas Ericsson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University West

University of Gothenburg

Computational Methods in Applied Mathematics

1609-4840 (ISSN) 1609-9389 (eISSN)

Vol. 21 4 791-810

Subject Categories

Computational Mathematics

Other Mathematics

Mathematical Analysis



More information

Latest update

4/5/2022 5