Parametric Finite Element Discretization of the Surface Stokes Equations

Abstract

We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the choice of discretization of the diffusion term and of the divergence term on numerical accuracy and convergence, as well as on implementation advantages, is discussed. We analyze the inf-sup stability of the discrete scheme in a generic approach by lifting stable finite element pairs known from the literature. A discretization error analysis in tangential norms then shows optimal order convergence of an isogeometric setting that requires only geometric knowledge of the discrete surface.

40 pages, 14 figures

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Cited by in corpus (3)

• A curvilinear surface ALE formulation for self-evolving Navier-Stokes manifolds - Stabilized finite element formulation
• Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces
• A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface