The divergence‐free nonconforming virtual element method for the <scp>Navier–Stokes</scp> problem
Bei Zhang, Jikun Zhao, Meng Li
Abstract
Abstract We 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 L 2 ‐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.
Topics & Concepts
Divergence (linguistics)Convergence (economics)MathematicsStokes problemElement (criminal law)Projection (relational algebra)Finite element methodOperator (biology)Applied mathematicsRate of convergenceMathematical analysisMathematical optimizationAlgorithmComputer sciencePhysicsKey (lock)ThermodynamicsPhilosophyChemistryTranscription factorEconomicsPolitical scienceBiochemistryComputer securityEconomic growthLinguisticsLawGeneRepressorAdvanced Numerical Methods in Computational MathematicsNumerical methods in engineeringNumerical methods in inverse problems