Virtual Elements for the Navier-Stokes problem on polygonal meshes
This work provides a novel numerical method for solving Navier-Stokes equations on complex polygonal meshes, offering improved accuracy and flexibility over traditional finite elements.
The paper proposes and analyzes a family of Virtual Element Methods for 2D Navier-Stokes equations on polygonal meshes, achieving point-wise divergence-free velocity fields with optimal convergence rates confirmed by numerical tests.
A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free. A rigorous error analysis is developed, showing that the methods are stable and optimally convergent. Several numerical tests are presented, confirming the theoretical predictions. A comparison with some mixed finite elements is also performed.