Analysis of the Taylor-Hood surface finite element method for the surface Stokes equation
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- by Arnold Reusken;
- Math. Comp. 94 (2025), 1701-1719
- DOI: https://doi.org/10.1090/mcom/4008
- Published electronically: August 15, 2024
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Abstract:
We consider the surface Stokes equation on a smooth closed hypersurface in $\mathbb {R}^3$. 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.References
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Bibliographic Information
- Arnold Reusken
- Affiliation: Institut für Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany
- MR Author ID: 147305
- ORCID: 0000-0002-4713-9638
- Email: reusken@igpm.rwth-aachen.de
- Received by editor(s): January 7, 2024
- Received by editor(s) in revised form: June 30, 2024
- Published electronically: August 15, 2024
- Additional Notes: The author was supported by the German Research Foundation (DFG) within the Research Unit “Vector- and tensor valued surface PDEs” (FOR 3013) with project no. RE 1461/11-2.
- © Copyright 2024 American Mathematical Society
- Journal: Math. Comp. 94 (2025), 1701-1719
- MSC (2020): Primary 65N12, 65N15, 65N30
- DOI: https://doi.org/10.1090/mcom/4008