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arXiv · 2302.00779

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

Maxim A. Olshanskii·Arnold Reusken·Paul Schwering
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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.

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Maxim A. Olshanskii, Arnold Reusken, Paul Schwering. 2023-02-01. An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces. https://arxiv.org/abs/2302.00779

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