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

被引：16

作者：

Brandner, Philip ^{[1
]}

Jankuhn, Thomas ^{[1
]}

Praetorius, Simon ^{[2
]}

Reusken, Arnold ^{[1
]}

Voigt, Axel ^{[2
,3
,4
]}

机构：

[1] Rhein Westfal TH Aachen, Inst Geometr & Prakt Math, D-52056 Aachen, Germany

[2] Tech Univ Dresden, Inst Wissensch Liches Rechnen, D-01062 Dresden, Germany

[3] Ctr Syst Biol Dresden CSBD, D-01307 Dresden, Germany

[4] Tech Univ Dresden, Cluster Excellence Phys Life, D-01062 Dresden, Germany

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2022年 / 44卷 / 04期

关键词：

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

D O I：

10.1137/21M1403126

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：A1807 / A1832

页数：26

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