Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations

TL;DR

This paper compares TraceFEM and SFEM discretization methods for surface Stokes equations, analyzing their efficiency and presenting higher order methods in a unified framework.

Contribution

It introduces a unified framework for higher order TraceFEM and SFEM methods applied to surface Stokes problems, including systematic comparison and efficiency analysis.

Findings

TraceFEM and SFEM are effectively applied to surface Stokes equations.

Higher order methods improve accuracy in discretization.

Benchmark results demonstrate the performance differences between formulations.

Abstract

In this paper we study parametric TraceFEM and parametric SurfaceFEM (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.