## A Reduced Basis Method for Parabolic Partial Differential Equations with Parameter Functions and Applications to Option Pricing

- Antonia Mayerhofer, ANTONIA MAYERHOFER
- 2014

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@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} }

- Published 2014 in Math. Comput.
DOI:10.1090/S0025-5718-2013-02782-2

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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