Abstract
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.
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