493	RWTH Publication No: 768786        2019        IGPM493.pdf
TITLE	Finite element error analysis of surface Stokes equations in stream function formulation
AUTHORS	Philip Brandner, Arnold Reusken
ABSTRACT	We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface Γ ⊂ R3 without boundary. This formulation leads to a coupled system of two second order scalar surface partial differential equations (for the stream function and an auxiliary variable). To this coupled system a trace finite element discretization method is applied. The main topic of the paper is an error analysis of this discretization method, resulting in optimal order discretization error bounds. The analysis applies to the surface finite element method of DziukElliott, too. We also investigate methods for reconstructing velocity and pressure from the stream function approximation. Results of numerical experiments are included.
KEYWORDS	surface Stokes, stream function formulation, error analysis, TraceFEM
DOI	10.1051/m2an/2020044
PUBLICATION	ESAIM: M2AN Volume 54, Number 6, November-December 2020