Finite Element Discretization Methods for Velocity-Pressure and Stream Function Formulations of Surface Stokes Equations

SIAM Journal on Scientific Computing, vol. 44, pp. A1807–A1832

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.

Authors 4

1. Thomas Jankuhn Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany

2. Simon Praetorius

   Technische Universität Dresden

   Affiliation as printed

   Institut für Wissenschaftliches Rechnen, TU Dresden, D-01062 Dresden, Germany

3. Arnold Reusken Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH-Aachen University, D-52056 Aachen, Germany

4. Axel Voigt

   Center for Systems Biology Dresden · Physics of Life · Technische Universität Dresden

   Affiliation as printed

   Institut für Wissenschaftliches Rechnen, TU Dresden, D-01062 Dresden, Germany, Center for Systems Biology Dresden (CSBD), Pfotenhauerstr. 108, 01307 Dresden, Germany and Cluster of Excellence -Physics of Life,

   TU Dresden, 01062 Dresden, Germany