Finite Element Discretization Methods for Velocity-Pressure and Stream Function Formulations of Surface Stokes Equations
Philip Brandner, Thomas Jankuhn, Simon Praetorius, Arnold Reusken, Axel Voigt
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.
Topics & Concepts
MathematicsDiscretizationFinite element methodStream functionStokes problemParametric statisticsStokes flowMathematical analysisApplied mathematicsSurface (topology)Mixed finite element methodFunction (biology)Scalar (mathematics)Extended finite element methodMathematical optimizationGeometryFlow (mathematics)MechanicsVorticityPhysicsEvolutionary biologyBiologyVortexThermodynamicsStatisticsAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsNumerical methods for differential equations