An improved error bound for reduced basis approximation of linear parabolic problems

@article{Urban2014AnIE,
  title={An improved error bound for reduced basis approximation of linear parabolic problems},
  author={Karsten Urban and Anthony T. Patera},
  journal={Math. Comput.},
  year={2014},
  volume={83},
  pages={1599-1615}
}
We consider a space-time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov-Galerkin truth finite element discretization with favorable discrete inf-sup constant βδ, the inverse of which enters into error estimates: βδ is unity for the heat equation; βδ decreases only linearly in time for non-coercive (but asymptotically stable) convection operators. The latter in turn permits effective long-time a posteriori error bounds for reduced… CONTINUE READING
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