Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds

Thomas Peter Fries*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Stationary and instationary Stokes and Navier-Stokes flows are considered on two-dimensional manifolds, ie, on curved surfaces in three dimensions. The higher-order surface FEM is used for the approximation of the geometry, velocities, pressure, and Lagrange multiplier to enforce tangential velocities. Individual element orders are employed for these various fields. Streamline-upwind stabilization is employed for flows at high Reynolds numbers. Applications are presented, which extend classical benchmark test cases from flat domains to general manifolds. Highly accurate solutions are obtained, and higher-order convergence rates are confirmed.

Original languageEnglish
Pages (from-to)55-78
Number of pages24
JournalInternational Journal for Numerical Methods in Fluids
Issue number2
Publication statusPublished - 20 Sept 2018


  • higher-order FEM
  • manifold
  • Navier-Stokes
  • Stokes
  • surface FEM
  • surface PDEs

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

Fields of Expertise

  • Human- & Biotechnology


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