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

2020/08/17 by Niklas Ericsson, Ericsson, N.
Computer Science · Earth and Planetary Sciences · Engineering · #65T99 #76D07 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.2008.07608

openalex publication_date 2020/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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