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.
Beirao da Veiga, L., Lovadina, C., Vacca, G. (2018). Virtual elements for the navier-stokes problem on polygonal meshes. SIAM JOURNAL ON NUMERICAL ANALYSIS, 56(3), 1210-1242 [10.1137/17M1132811].
Virtual elements for the navier-stokes problem on polygonal meshes
Beirao da Veiga, L;VACCA, GIUSEPPE
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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10.113717M1132811.pdf
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2018-Beirao_Lovadina_Vacca-SINUM.pdf
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