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

Research output: Contribution to journalResearch articleContributedpeer-review



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.


Original languageEnglish
Article number4
Pages (from-to)A1807-A1832
JournalSIAM Journal of Scientific Computing
Issue number4
Publication statusPublished - 5 Jul 2022

External IDs

Scopus 85131602137
Mendeley be83627a-a729-3134-9ad5-10e6f7ac44bb
dblp journals/siamsc/BrandnerJPRV22
WOS 000863909200001


DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis


  • surface Stokes equation, trace finite element method, TraceFEM, Surface Finite Elements, Taylor-Hood finite elements, stream function formulation, higher order surface approximation, surface finite element method, VORTICES, PDES, IMPLICIT GEOMETRIES, MOTION, INTERFACE, ERROR ANALYSIS, NAVIER-STOKES, DYNAMICS, FLOWS, DOMAINS

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