Abstract
AbstractWe present the divergence‐free nonconforming virtual element method for the Navier–Stokes problem. By using a gradient projection operator, we construct a nonconforming virtual element that allows us to compute the L2‐projection. The nonconforming virtual element provides the exact divergence‐free approximation to the velocity and is proved to be convergent with the optimal convergence rate. Finally, the numerical results are shown to confirm the convergence of the nonconforming virtual element.
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