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arXiv · 2508.19198

A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface

Harald Garcke·Robert Nürnberg
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Abstract

In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell \geq 2$. In the semidiscrete continuous-in-time setting we are able to prove a stability estimate that mimics a corresponding result for the continuous problem. Some numerical results, including a convergence experiment, demonstrate the practicality and accuracy of the proposed method.

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Harald Garcke, Robert Nürnberg. 2025-08-26. A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface. https://doi.org/10.4208/cicp.oa-2025-0221

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