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

02/01/2023

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by   Maxim A. Olshanskii, et al.

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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 ℝ^3. 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.