A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain
Artikel i vetenskaplig tidskrift, 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

Författare

Niklas Ericsson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Högskolan Väst

Göteborgs universitet

Computational Methods in Applied Mathematics

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

Vol. In Press

Ämneskategorier

Beräkningsmatematik

Annan matematik

Matematisk analys

DOI

10.1515/cmam-2020-0129

Mer information

Senast uppdaterat

2021-04-27