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arXiv · 2401.03561

Analysis of the Taylor-Hood Surface Finite Element Method for the surface Stokes equation

Arnold Reusken
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Abstract

We consider the surface Stokes equation on a smooth closed hypersurface in three-dimensional space. For discretization of this problem a generalization of the surface finite element method (SFEM) of Dziuk-Elliott combined with a Hood-Taylor pair of finite element spaces has been used in the literature. We call this method Hood-Taylor-SFEM. This method uses a penalty technique to weakly satisfy the tangentiality constraint. In this paper we present a discretization error analysis of this method resulting in optimal discretization error bounds in an energy norm. We also address linear algebra aspects related to (pre)conditioning of the system matrix.

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Arnold Reusken. 2024-01-07. Analysis of the Taylor-Hood Surface Finite Element Method for the surface Stokes equation. https://arxiv.org/abs/2401.03561

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