FINITE ELEMENT DISCRETIZATION METHODS FOR VELOCITY-PRESSURE AND STREAM FUNCTION FORMULATIONS OF SURFACE STOKES EQUATIONS

In this paper we study parametric trace finite element (TraceFEM) and parametric surface finite element (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.

Automated summary

In this paper, the parametric trace finite element (TraceFEM) and parametric surface finite element (SFEM) discretizations of a surface Stokes problem were studied. Higher order methods were presented in a unified framework and applied to both the velocity-pressure formulation and the stream function formulation of the Stokes problem. The numerical efficiency of the two formulations was discussed and a systematic comparison between TraceFEM and SFEM was provided. A benchmark problem with a scalar reference quantity was introduced and numerically determined.