A family of virtual element methods for the two-dimensional Navier-Stokes equations is proposed and analyzed. The schemes provide a discrete velocity field which is pointwise 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.
Virtual elements for the navier-stokes problem on polygonal meshes / L. Beirao da Veiga, C. Lovadina, G. Vacca. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 56:3(2018), pp. 1210-1242.
Virtual elements for the navier-stokes problem on polygonal meshes
L. Beirao da Veiga;C. Lovadina;
2018
Abstract
A family of virtual element methods for the two-dimensional Navier-Stokes equations is proposed and analyzed. The schemes provide a discrete velocity field which is pointwise 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.
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