A new error bound for reduced basis approximation of parabolic partial differential equations
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Patera_A new error bound.pdf
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Author(s)
Urban, Karsten
Patera, Anthony T.
Date Issued
February 2012
Journal
Comptes Rendus Mathematique
Publisher
Elsevier
Citation
Urban, Karsten, and Anthony T. Patera. “A New Error Bound for Reduced Basis Approximation of Parabolic Partial Differential Equations.” Comptes Rendus Mathematique 350, no. 3–4 (February 2012): 203–207.
Version
Author's final manuscript
Abstract
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 β[subscript δ]:β[subscript δ] is unity for the heat equation; β[subscript δ] grows 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 basis approximations, in sharp contrast to classical (pessimistic) exponentially growing energy estimates.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-NoDerivatives
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DOI of Published Version
https://doi.org/10.1016/j.crma.2012.01.026
