2025/08/26 by Harald Garcke, Robert Nürnberg, Garcke, Harald +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Compressibility #Convergence (economics) #Finite element method #Numerical stability #Parametric statistics #Representation (politics) #Stability (learning theory) #Stability and Controllability of Differential Equations #Surface (topology) #cs.NA #math.NA
paper · pdf · doi:10.4208/cicp.oa-2025-0221
published in Communications in Computational Physics 40(4), 992-1018 (Cambridge University Press)
openalex publication_date 2026/07/01 · openalex created_date 2026/07/10 · openalex updated_date 2026/08/05
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.