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An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces (2302.00779v2)
Published 1 Feb 2023 in math.NA, cs.NA, math-ph, and math.MP
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 $\mathbb{R}3$. 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.