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

被引：21

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

共 77 条

[1]

Abraham R., 1988, Applied Mathematical Sciences, DOI 10.1007/978-1-4612-1029-0

[2] Lagrangian Navier-Stokes diffusions on manifolds: Variational principle and stability [J].

Arnaudon, Marc ;

Cruzeiro, Ana Bela .

BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (08) :857-881

[3]

Arnold V. I., 1989, Mathematical Methods of Classical Mechanics, V60

[4]

Arroyo M, 2009, PHYS REV E, V79, DOI 10.1103/PhysRevE.79.031915

[5] A stable numerical method for the dynamics of fluidic membranes [J].

Barrett, John W. ;

Garcke, Harald ;

Nurnberg, Robert .

NUMERISCHE MATHEMATIK, 2016, 134 (04) :783-822

[6] The DUNE framework: Basic concepts and recent developments [J].

Bastian, Peter ;

Blatt, Markus ;

Dedner, Andreas ;

Dreier, Nils-Arne ;

Engwer, Christian ;

Fritze, Rene ;

Graeser, Carsten ;

Grueninger, Christoph ;

Kempf, Dominic ;

Kloefkorn, Robert ;

Ohlberger, Mario ;

Sander, Oliver .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 81 :75-112

[7]

BONITO A., 2020, Handbook of Numerical Analysis, V21, P1

[8] A DIVERGENCE-CONFORMING FINITE ELEMENT METHOD FOR THE SURFACE STOKES EQUATION [J].

Bonito, Andrea ;

Demlow, Alan ;

Licht, Martin .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2020, 58 (05) :2764-2798

[9]

Brandner P., 2021, TRACEFEM STREAM FUNC, DOI [10.5281/zenodo.5681028, DOI 10.5281/ZENODO.5681028]

[10] Finite element error analysis of surface Stokes equations in stream function formulation [J].

Brandner, Philip ;

Reusken, Arnold .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2020, 54 (06) :2069-2097

← 1 2 3 4 5 6 7 8 →