Abstract
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in ℝ3. The method employs parametric Pk-Pk−1 finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin–Helmholtz instability problem on the unit sphere.
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Funding: The authors T. Jankuhn and A. Reusken wish to thank the German Research Foundation (DFG) for financial support within the Research Unit ‘Vector- and tensor valued surface PDEs' (FOR 3013) with project No. RE 1461/11-1. M. Olshanskii and A. Zhiliakov were partially supported by NSF through the Division of Mathematical Sciences grants 1717516 and 2011444.
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