Error analysis of higher order trace finite element methods for the surface Stokes equations
Numerical Analysis
2020-03-17 v1 Numerical Analysis
Abstract
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood 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.
Cite
@article{arxiv.2003.06972,
title = {Error analysis of higher order trace finite element methods for the surface Stokes equations},
author = {Thomas Jankuhn and Maxim A. Olshanskii and Arnold Reusken and Alexander Zhiliakov},
journal= {arXiv preprint arXiv:2003.06972},
year = {2020}
}
Comments
28 pages, 3 figures