621	RWTH Publication No: 976528        2024
TITLE	Analysis of the Taylor-Hood Surface Finite Element Method for the surface Stokes equation
AUTHORS	Arnold Reusken
ABSTRACT	We consider the surface Stokes equation on a smooth closed hypersurface in R3. For discretization of this problem a generalization of the surface finite element method (SFEM) of Dziuk-Elliott combined with a Hood-Taylor pair of finite element spaces has been used in the literature. We call this method Hood-Taylor-SFEM. This method uses a penalty technique to weakly satisfy the tangentiality constraint. In this paper we present a discretization error analysis of this method resulting in optimal discretization error bounds in an energy norm. We also address linear algebra aspects related to (pre)conditioning of the system matrix.
KEYWORDS	surface Stokes equation, Taylor-Hood finite element pair, finite element error analysis