A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations

@article{Grepl2005APE,
  title={A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations},
  author={Martin A. Grepl and Anthony T. Patera},
  journal={Mathematical Modelling and Numerical Analysis},
  year={2005},
  volume={39},
  pages={157-181}
}
  • M. Grepl, A. Patera
  • Published 2005
  • Mathematics, Computer Science
  • Mathematical Modelling and Numerical Analysis
In this paper, we extend the reduced-basis methods and associated a posteriori error estimators developed earlier for elliptic partial differential equations to parabolic problems with affine parameter dependence. The essential new ingredient is the presence of time in the formulation and solution of the problem - we shall "simply" treat time as an additional, albeit special, parameter. First, we introduce the reduced-basis recipe - Galerkin projection onto a space WN spanned by solutions of… 

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