# Stabilized reduced basis methods for parametrized steady Stokes and Navier-Stokes equations

@article{Ali2020StabilizedRB, title={Stabilized reduced basis methods for parametrized steady Stokes and Navier-Stokes equations}, author={Shafqat Ali and Francesco Ballarin and Gianluigi Rozza}, journal={ArXiv}, year={2020}, volume={abs/2001.00820} }

It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf-sup approximation stability even if a stable high fidelity method was used to generate snapshots. For problems in computational fluid dynamics, the lack of inf-sup stability is reflected by the inability to accurately approximate the pressure field. In this context, inf-sup stability is usually recovered through the enrichment of the velocity… CONTINUE READING

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