512	RWTH Publication No: 815287        2021        IGPM512.pdf
TITLE	Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations
AUTHORS	Philip Brandner, Thomas Jankuhn, Simon Praetorius, Arnold Reusken, Axel Voigt
ABSTRACT	In this paper we study parametric TraceFEM and parametric SurfaceFEM (SFEM) discretizations of a surface Stokes problem. These methods are applied both to the Stokes problem in velocity-pressure formulation and in stream function formulation. A class of higher order methods is presented in a unified framework. Numerical efficiency aspects of the two formulations are discussed and a systematic comparison of TraceFEM and SFEM is given. A benchmark problem is introduced in which a scalar reference quantity is defined and numerically determined.
KEYWORDS	surface Stokes equation, trace finite element method (TraceFEM), surface finite element method (SFEM), Taylor-Hood finite elements, stream function formulation, higher order surface approximation
DOI	10.1137/21M1403126
PUBLICATION	SIAM Journal on Scientific Computing, Vol. 44, Iss. 4 (2022)