An improved error bound for reduced basis approximation of linear parabolic problems
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Author(s)
Urban, Karsten
Patera, Anthony T.
Date Issued
October 2013
Journal
Mathematics of Computation
Publisher
American Mathematical Society (AMS)
Citation
Urban, Karsten, and Anthony T. Patera. “An Improved Error Bound for Reduced Basis Approximation of Linear Parabolic Problems.” Mathematics of Computation 83, no. 288 (October 23, 2013): 1599–1615. © 2013 American Mathematical Society
Version
Final published version
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], the inverse of which enters into error estimates: β[subscript δ] is unity for the heat equation; β[subscript δ] 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 basis approximations, in sharp contrast to classical (pessimistic) exponentially growing energy estimates. The paper contains a full analysis and various extensions for the formulation introduced briefly by Urban and Patera (2012) as well as numerical results for a model reaction-convection-diffusion equation.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1090/S0025-5718-2013-02782-2
