493 IGPM493.pdf        October 2019
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
Volume 54, Number 6, November-December 2020