|| IGPM493.pdf October 2019 |
|| Finite element error analysis of surface Stokes equations in stream function formulation |
||Philip Brandner, Arnold Reusken|
||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. |
|| surface Stokes, stream function formulation, error analysis, TraceFEM |