Divergence‐free tangential finite element methods for incompressible flows on surfaces

@article{Lederer2020DivergencefreeTF,
  title={Divergence‐free tangential finite element methods for incompressible flows on surfaces},
  author={Philip L. Lederer and Christoph Lehrenfeld and Joachim Sch{\"o}berl},
  journal={International Journal for Numerical Methods in Engineering},
  year={2020},
  volume={121},
  pages={2503 - 2533}
}
In this work we consider the numerical solution of incompressible flows on two‐dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the approximation of a velocity field that lies only in the tangential space of the given geometry. Abandoning H1‐conformity allows us to construct finite elements which are—due to an application of the Piola transformation—exactly tangential. To reintroduce… 
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