491

IGPM491.pdf September 2019 
TITLE 
Higher order trace finite element methods for the surface Stokes equation 
AUTHORS 
Thomas Jankuhn, Arnold Reusken 
ABSTRACT 
In this paper a class of higher order finite element methods for the discretization of
surface Stokes equations is studied. These methods are based on an unfitted finite element approach
in which standard TaylorHood spaces on an underlying bulk mesh are used. For treating the
constraint that the velocity must be tangential to the surface a penalty method is applied. Higher
order geometry approximation is obtained by using a parametric trace finite element technique,
known from the literature on trace finite element methods for scalar surface partial differential
equations. Based on theoretical analyses for related problems, specific choices for the parameters in
the method are proposed. Results of a systematic numerical study are included in which different
variants are compared and convergence properties are illustrated. 
KEYWORDS 
surface Stokes equation, trace finite element method, TaylorHood finite elements 