| Issue |
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
|
|
|---|---|---|
| Page(s) | 1177 - 1211 | |
| DOI | https://doi.org/10.1051/m2an/2025025 | |
| Published online | 25 April 2025 | |
A C0 interior penalty method for the stream function formulation of the surface Stokes problem
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
* Corresponding author: neilan@pitt.edu
Received:
12
December
2024
Accepted:
29
March
2025
We propose a C0 interior penalty method for the fourth-order stream function formulation of the surface Stokes problem. The scheme utilizes continuous, piecewise polynomial spaces defined on an approximate surface. We show that the resulting discretization is positive definite and derive error estimates in various norms in terms of the polynomial degree of the finite element space as well as the polynomial degree to define the geometry approximation. A notable feature of the scheme is that it does not explicitly depend on the Gauss curvature of the surface. This is achieved via a novel integration-by-parts formula for the surface biharmonic operator.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30
Key words: Surface Stokes / streamfunction / interior penalty
© The authors. Published by EDP Sciences, SMAI 2025
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