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

2025/08/26 by Harald Garcke, Robert Nürnberg, Garcke, Harald +1 · 1 citation
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paper · pdf · doi:10.4208/cicp.oa-2025-0221

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 ℓ ≥ 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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