Higher order Trace Finite Element Methods for the Surface Stokes Equation

Abstract

In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying bulk mesh are used. For treating the constraint that the velocity must be tangential to the surface a penalty method is applied. Higher order geometry approximation is obtained by using a parametric trace finite element technique, known from the literature on trace finite element methods for scalar surface partial differential equations. Based on theoretical analyses for related problems, specific choices for the parameters in the method are proposed. Results of a systematic numerical study are included in which different variants are compared and convergence properties are illustrated.

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Cited by in corpus (8)

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• Parametric Finite Element Discretization of the Surface Stokes Equations
• Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces
• Error analysis of higher order trace finite element methods for the surface Stokes equations
• A Higher-order Trace Finite Element Method for Shells