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Adaptive variational multiscale methods for incompressible flow based on two local Gauss integrations. (English) Zbl 1425.76067
Summary: We consider variational multiscale (VMS) methods with \(h\)-adaptive technique for the stationary incompressible Navier-Stokes equations. The natural combination of VMS with adaptive strategy retains the best features of both methods and overcomes many of their deficits. A reliable a posteriori projection error estimator is derived, which can be computed by two local Gauss integrations at the element level. Finally, some numerical tests are presented to illustrate the method’s efficiency.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76M30 Variational methods applied to problems in fluid mechanics
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FreeFem++
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