| Issue |
ESAIM: M2AN
Volume 54, Number 6, November-December 2020
|
|
|---|---|---|
| Page(s) | 2069 - 2097 | |
| DOI | https://doi.org/10.1051/m2an/2020044 | |
| Published online | 12 October 2020 | |
Research Article
Finite element error analysis of surface Stokes equations in stream function formulation
Institut für Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany
* Corresponding author: brandner@igpm.rwth-aachen.de, philip.brandner@rwth-aachen.de
Received:
21
October
2019
Accepted:
29
June
2020
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface Γ ⊂ ℝ3 without boundary. This formulation leads to a coupled system of two second order scalar surface partial differential equations (for the stream function and an auxiliary variable). To this coupled system a trace finite element discretization method is applied. The main topic of the paper is an error analysis of this discretization method, resulting in optimal order discretization error bounds. The analysis applies to the surface finite element method of Dziuk–Elliott, too. We also investigate methods for reconstructing velocity and pressure from the stream function approximation. Results of numerical experiments are included.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15
Key words: Surface Stokes / stream function formulation / error analysis / TraceFEM
© EDP Sciences, SMAI 2020
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