2022/12/29 by Claudio Canuto, Canuto, Claudio, Davide Rosso +1
Engineering · Physics and Astronomy · #65N30 #76D05 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2212.14414
openalex publication_date 2022/12/29 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28
We consider the Virtual Element method (VEM) introduced by Beirão da Veiga, Lovadina and Vacca in 2016 for the numerical solution of the steady, incompressible Navier-Stokes equations; the method has arbitrary order k ≥ 2 and guarantees divergence-free velocities. For such discretization, we develop a residual-based a posteriori error estimator, which is a combination of standard terms in VEM analysis (residual terms, data oscillation, and VEM stabilization), plus some other terms originated by the VEM discretization of the nonlinear convective term. We show that a linear combination of the velocity and pressure errors is upper-bounded by a multiple of the estimator (reliability). We also establish some efficiency results, involving lower bounds of the error. Some numerical tests illustrate the performance of the estimator and of its components while refining the mesh uniformly, yielding the expected decay rate. At last, we apply an adaptive mesh refinement strategy to the computation of the low-Reynolds flow around a square cylinder inside a channel.