Reduced Basis Error Bound Computation of Parameter-Dependent Navier-Stokes Equations by the Natural Norm Approach

@article{Deparis2008ReducedBE,
  title={Reduced Basis Error Bound Computation of Parameter-Dependent Navier-Stokes Equations by the Natural Norm Approach},
  author={Simone Deparis},
  journal={SIAM J. Numerical Analysis},
  year={2008},
  volume={46},
  pages={2039-2067}
}
This work focuses on the a posteriori error estimation for the reduced basis method applied to partial differential equations with quadratic nonlinearity and affine parameter dependence. We rely on natural norms—local parameter-dependent norms—to provide a sharp and computable lower bound of the inf-sup constant. We prove a formulation of the Brezzi–Rappaz–Raviart existence and uniqueness theorem in the presence of two distinct norms. This allows us to relax the existence condition and to… CONTINUE READING

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