An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces

  • Olshanskii, Maxim (University of Houston)
  • Reusken, Arnold (RWTH Aachen)

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We introduce a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in R^3. The discrete formulation employs finite difference and finite elements methods to handle evolution in time and variation in space, respectively. We present a numerical analysis of the method, which includes stability, optimal order convergence, and quantification of the geometric errors.