523	RWTH Publication No: 918215        2023        IGPM523.pdf
TITLE	An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces
AUTHORS	Maxim A. Olshanskii, Arnold Reusken, Paul Schwering
ABSTRACT	The paper introduces 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 ℝ3. The discrete formulation employs finite difference and finite elements methods to handle evolution in time and variation in space, respectively. A complete numerical analysis of the method is presented, including stability, optimal order convergence, and quantification of the geometric errors. Results of numerical experiments are also provided.
KEYWORDS	surface Navier–Stokes system, surface PDEs, evolving surfaces, TraceFEM