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

2020/03/16 by Thomas Jankuhn, Maxim A. Olshanskii, Jankuhn, Thomas +5 · 4 citations
Engineering · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2003.06972

openalex publication_date 2020/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A continuum theory of elastic material surfaces

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• Surface Stokes Without Inf-Sup Condition
• A Taylor-Hood finite element method for the surface Stokes problem without penalization

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