Error analysis of higher order trace finite element methods for the surface Stokes equations

arXiv (Cornell University)

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.

Authors 4

1. Thomas Jankuhn Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Maxim A. Olshanskii

   University of Houston

   Affiliation as printed

   University of Houston

3. Arnold Reusken Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

4. Alexander Zhiliakov

   University of Houston

   Affiliation as printed

   University of Houston