
Finite Element Error Analysis of Surface Stokes Equations in Stream Function Formulation
We consider a surface Stokes problem in stream function formulation on a...
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On derivations of evolving surface NavierStokes equations
In recent literature several derivations of incompressible NavierStokes...
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Multiscale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains
In this paper, we study a multiscale deep neural network (MscaleDNN) as...
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Continuous data assimilation applied to a velocityvorticity formulation of the 2D NavierStokes equations
We study a continuous data assimilation (CDA) algorithm for a velocityv...
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Higherorder surface FEM for incompressible NavierStokes flows on manifolds
Stationary and instationary Stokes and NavierStokes flows are considere...
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On Fourier analysis of polynomial multigrid for arbitrary multistage cycles
The Fourier analysis of the pmultigrid acceleration technique is consid...
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Optimal sensing for fish school identification
Fish schooling implies an awareness of the swimmers for their companions...
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Finite element discretization methods for velocitypressure and stream function formulations of surface Stokes equations
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 velocitypressure 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.
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