Error analysis of higher order Trace Finite Element Methods for the surface Stokes equation

Journal of Numerical Mathematics, vol. 29, pp. 245–267

Abstract

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 P k -P k−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.

Authors 4

1. Thomas Jankuhn Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH-Aachen University , D-52056 , Aachen , Germany

2. Maxim A. Olshanskii

   University of Houston

   Affiliation as printed

   Department of Mathematics , University of Houston , Houston , Texas 77204 , USA

3. Arnold Reusken corresponding Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH-Aachen University , D-52056 , Aachen , Germany

4. Alexander Zhiliakov

   University of Houston

   Affiliation as printed

   Department of Mathematics , University of Houston , Houston , Texas 77204 , USA