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|a Urban, Karsten
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|a Massachusetts Institute of Technology. Department of Mechanical Engineering
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|a Patera, Anthony T.
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|a Patera, Anthony T.
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|a An improved error bound for reduced basis approximation of linear parabolic problems
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|b American Mathematical Society (AMS),
|c 2015-07-07T16:03:52Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/97697
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|a 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.
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|a United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613)
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|a United States. Office of Naval Research (Grant N00014-11-1-0713)
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|a Article
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|t Mathematics of Computation
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