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

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.

28 pages

Cited by in corpus (10)

• A numerical approach for fluid deformable surfaces with conserved enclosed volume
• Tangential Errors of Tensor Surface Finite Elements
• Coordinated motion of epithelial layers on curved surfaces
• The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics
• Parametric Finite Element Discretization of the Surface Stokes Equations
• Diffusion of tangential tensor fields: numerical issues and influence of geometric properties
• Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces
• Phase-separated lipid vesicles: continuum modeling, simulation, and validation
• Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods
• A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface