A framework for approximation of the Stokes equations in an axisymmetric domain

N. Ericsson

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arXiv · 2008.07608

A framework for approximation of the Stokes equations in an axisymmetric domain

N. Ericsson

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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.

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N. Ericsson. 2020-08-17. A framework for approximation of the Stokes equations in an axisymmetric domain. https://arxiv.org/abs/2008.07608

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