Affiliation:
1. Department of Engineering Science , University West , SE–461 86 Trollhättan ; and Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE–412 96 Gothenburg , Sweden
Abstract
Abstract
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.
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis
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